Would you please explain to me whether Hebrews 10:26 is speaking about a believer losing his or her salvation?
Hebrews 10:26 can only be understood in its near context (and in the context of the book of Hebrews). Paul's essential purpose in writing this book is to pull Jewish believers away from continuing in the temple ritual now that that ritual had been fulfilled in the incarnation, life, and sacrifice of Jesus Christ. For to continue with an elaborate system of rituals which spoke of the coming Savior and His future death on the cross was to say, in effect, that Jesus was not the Messiah and His death not valid. Continuation in the foreshadowing ritual after the real Christ had come and suffered in the flesh for real was tantamount to denying and disowning Him, and would eventually destroy the faith of those who persisted in the practice. Paul did not come to this realization at once (cf. the development of his understanding of true baptism as Spirit baptism: 1Cor.1:17). Indeed, his imprisonment, chronicled in the book of Acts, is a result of his persistence, for sentimental and "practical" reasons, in these rituals he loved. He had been warned not to go up to Jerusalem "through the Spirit" (Acts 21:4; cf. Acts 21:10-11), and then had agreed to sponsor the vows of some young men to show that "he lived in obedience to the [Mosaic] law" (Acts 21:24), which he certainly did not (1Cor.9:20-21). This was a blind spot, and a compromise, and Paul had previously pointed this out in the case of others (cf. Gal.2:11-14). To be fair, Paul is the first one of whom we know (apostle or otherwise) to even come to understand this issue with clarity (let alone to successfully explain it). And given that the primary features of the Roman Catholic and Greek Orthodox faiths (not to mention to a very large degree many Protestant denominations) are still largely based upon emulating, adopting, copying or transforming the Jewish rituals (i.e., priests, incense censors, churches with paraphernalia resembling the temple, altars so that communion set in a sacrificial context, etc.), we can see that this was no small accomplishment. Whatever compromise Paul had been involved in is more than set straight by the book of Hebrews which explodes virtually every aspect of the argument for Jewish believers to continue in the traditional manner of worship. This overarching thesis of the book of Hebrews is at the center of the interpretation of Heb.10:26 (set here in a wider context):
(19) Therefore, brothers, since we have confidence in this entrance of ours into the [heavenly] holy of holies by the blood of Jesus, (20) an entryway through the [heavenly] veil [of separation] which is new and alive and which He has consecrated for us, that is [through the sacrifice] of His flesh (cf. Heb.10:10; 10:18), (21) and since we have [this] great high priest over the household of God, let us approach [the throne of grace (cf. Heb.4:16) to pray] with a truthful heart in complete faith, (22) our hearts sprinkled [clean] of [any] bad conscience and our bodies washed with pure water [of the Word (cf. Eph.5:26)]. (23) Let us hold on without turning [to the right or to the left] to the hope we have professed - for the One who has promised us [eternal life] is faithful. (24) And let us give careful attention to one another['s ministries] as motivation for [our own] love and good works, (25) not abandoning your mutual assembling (as some have made it their practice to do [and which makes this impossible]), but rather encouraging each other [to persevere in this work of the Lord], and doing so to an ever greater degree to the extent that you see the day [of the Lord] drawing [ever] closer. (26) For if we willfully continue in the life of sin after accepting and recognizing the truth [of the gospel], there remains no further sacrifice we can make for our sins, (27) but only a terrible expectation of judgment, and a burning fire, ready to devour those who oppose [His will]. (28) For anyone who set aside the law of Moses perished without mercy on the [testimony] of two or three witnesses. (29) How much greater punishment do you suppose will not justly come to someone who has trampled the Son of God underfoot, and who has considered His blood of the covenant to be unclean (the very blood by which you were sanctified), and who has violently insulted the Spirit of grace?
The last sentence here is the conclusion for this whole section. We see here what Paul means in the near context when he says above in the verse you ask about, verse 26, "if we willfully continue in the life of sin after accepting and recognizing the truth (of the gospel), there remains no further sacrifice we can make for our sins". In other words, by continuing in the Jewish temple ritual, these Jewish believers were committing sin, and serious sin at that. Because every time they participated in an animal sacrifice, they were saying, in effect, that Jesus died in vain. This really is "trampling" Him under foot; this really is regarding His blood, that is, His death on the cross, as "unclean", this really is "violently insulting" the Spirit who testifies to Him and to the validity of His work.
There were certainly reasons that the Jewish believers in Jerusalem were drawn to these things: tradition, nostalgia, the desire to avoid confrontation with (and persecution by) unbelievers who expected it of them. But Paul lets these backsliding believers know in no uncertain terms that to continue in these practices will be the death of their faith. All sin endangers faith, because all sin is lawlessness (1Jn.3:4). If we are walking in the light (1Jn.1:7), we can confess our failings and be confident of forgiveness (1Jn.1:9). But if we are not walking in the light, that is, if we are involved in a pattern of rebellion, a pattern of sinful conduct we know to be sinful, if we willfully and arrogantly disobey God long and hard enough, then we have no fellowship with God (1Jn.1:6), and our hearts eventually become hardened to Him, and our faith decays and eventually dies - and without faith there is no salvation (cf. Matt.10:33; Lk.14:34-35; Jn.15:5-6; Rom.11:17-23; 1Cor.6:9-11; 10:6-12; 15:2; 2Cor.13:5; Gal.5:19-21; Eph.5:3-7; Col.1:21-23; 1Tim.6:9; 6:20-21; 2Tim.2:12; Heb.2:1-3; 3:6-19; 10:35-39; 2Jn.1:8-9). So while the specific application of Hebrews 10:26 "if we willfully continue in the life of sin" is to this particular pattern of sinning, any pattern of choosing a life of sin against God will lead eventually and inevitably to the same place:
(12) Make sure, brothers, that none of you develop an evil heart of unbelief (i.e., lack of faith) by turning away (lit. "apostatizing") from the living God. (13) Rather keep encouraging each other every day as long as we still call it "today" (i.e. still remain in this world), lest any of you be hardened [in heart] by the deception of sin. (14) For we all have a share in Christ, as long as we hang on to that original confidence [of our faith] firmly to the end, (15) as it says: "Today if you hear His voice, Don't harden your hearts as they did at the provocation [at Meribah]." (16) For who provoked Him, though they had heard? Did not all of them who came out of Egypt under Moses' leadership do so? (17) And with whom was He enraged for forty years? Wasn't it the very people who had sinned, then dropped dead in the desert? (18) And to whom did He swear that they would never enter into the [place of] rest [He had promised], but to those who had been disobedient to Him? (19) Now we see that they were unable to enter into this [place of rest] because of their unbelief (i.e., their loss of faith).
Every one is tempted by his own lust, being dragged away [by it] and enticed [by it]. Then, should lust conceive (i.e., should the person give in to it), it gives birth to sin. And sin, should it be fully carried out to the end (i.e., should the person give in to a life of sin), produces death (i.e., the death of faith).
If anyone sees his brother sinning a sin (i.e., involved in sin) which is not unto death (i.e., is a deviation rather than a complete turning away), let him ask [forgiveness on his brother's behalf], and life will be given to him (i.e., forgiveness and deliverance), that is, in those cases where those sinning are not [sinning] unto death (i.e., engaged in a willful process of "deadly" faith destroying sinfulness).
1st John 5:16
Let us not put Christ to the test, as some of them (i.e., the Exodus generation) did and were killed by serpents. And let us not be complaining, as some of them complained, and were killed by the Destroyer. These things happened to them as an example to us and were written to warn us (i.e., to avoid similar apostasy) – we who live at the culmination of the ages (i.e., at the doorstep of the Tribulation). So let him who thinks he stands firm beware lest he fall (i.e., from faith; cf. Rom.11:22).
1st Corinthians 10:11-12
Don't you understand that if you give your allegiance to anyone to obey them as servants, then you truly are their servants when you obey them? [This is true] whether [you give yourselves] to sin, which results in death (i.e., of faith ), or whether [you give yourselves] to obedience [to Christ], which results in righteousness?
For more on the topic please see the links:
Have I Lost my Salvation? (part II)
Hebrews 10:26 again.
Deliberate Sinning in Hebrews 10:26.
Have I Lost my Salvation?
Sin, Confession and Forgiveness.
Sin and Spiritual Transformation.
Sin and Forgiveness.
Recovering from Sin.
The Victory of Faith
Apostasy and the Sin unto Death, the Conscience and Sanctification.
The Sin Problem, Unbelievers, and Hardness of Heart (in BB 4B: Soteriology).
In Your Anger, do not Sin: Ephesians 4:26 and the Sin Nature.
The Saved and the Unsaved
Apostasy and the Sin unto Death (in BB 3B: Hamartiology: the study of sin)
The Great Apostasy (in "Coming Tribulation" Part 3A)
Peter's Epistles: lesson #21: Perseverance of Faith
Peter's Epistles: lesson #26: Reactions to Personal Tribulation
Peter's Epistles: lesson #27: Three False Doctrines that Threaten Faith
In Him in whom we glory and whom we shall never be ashamed to confess, our Lord and Savior Jesus Christ.