This is the traditional Adventist teaching in as much of a nutshell as I can fit it into; it is very complex and difficult to explain briefly.
Keep in mind that I am summarizing it, not agreeing with it.
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There is a sanctuary in heaven with two "apartments" or rooms, just like the tabernacle on earth: the holy place and the most holy place. When Jesus ascended to heaven after the resurrection, He entered the holy place and transferred the confessed sins of believers there by His own blood. This is how Ellen White describes it:
As the sins of the people were anciently transferred, in figure, to the earthly sanctuary by the blood of the sin-offering, so our sins are, in fact, transferred to the heavenly sanctuary by the blood of Christ. And as the typical cleansing of the earthly was accomplished by the removal of the sins by which it had been polluted, so the actual cleansing of the heavenly is to be accomplished by the removal, or blotting out, of the sins which are there recorded. This necessitates an examination of the books of record to determine who, through repentance of sin and faith in Christ, are entitled to the benefits of his atonement. The cleansing of the sanctuary therefore involves a work of investigative Judgment. This work must be performed prior to the coming of Christ to redeem his people; for when he comes, his reward is with him to give to every man according to his works. [REV. 22:12.] {4SP 266.1}
In the OT sacrificial system, when a person sinned and brought an animal as a sacrifice for his sin, that sin was first confessed and transferred to the animal, and then the sin was transferred from the animal to the sanctuary via the administration of the animal's shed blood in the holy place. Those sins, recorded in blood, would build up all year long, defiling the sanctuary, until the Day of Atonement. On that day, the high priest would enter the most holy place to cleanse it from all of the sins that had accumulated that year.
Since the earthly tabernacle was a pattern of the heavenly, there is a corresponding "antitypical" fulfillment of all of the OT ceremonies. Jesus fulfilled the sacrificial system and the spring feasts (Passover, Firstfruits, Pentecost) at the time of His death and resurrection, but the fall feasts (Trumpets, Day of Atonement, Feast of Tabernacles) had yet to be fulfilled in the future. After His ascension, Jesus began His priestly work in the holy place of the heavenly sanctuary, where He remained until 1844. Here is Ellen White's description of what He was doing there:
Such was the service performed "unto the example and shadow of heavenly things." And what was done in type in the ministration of the earthly sanctuary is done in reality in the ministration of the heavenly sanctuary. After His ascension our Saviour began His work as our high priest. Says Paul: "Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us." Hebrews 9:24. {GC 420.2}
The ministration of the priest throughout the year in the first apartment of the sanctuary, "within the veil" which formed the door and separated the holy place from the outer court, represents the work of ministration upon which Christ entered at His ascension. It was the work of the priest in the daily ministration to present before God the blood of the sin offering, also the incense which ascended with the prayers of Israel. So did Christ plead His blood before the Father in behalf of sinners, and present before Him also, with the precious fragrance of His own righteousness, the prayers of penitent believers. Such was the work of ministration in the first apartment of the sanctuary in heaven. {GC 420.3}
Thither the faith of Christ's disciples followed Him as He ascended from their sight. Here their hopes centered, "which hope we have," said Paul, "as an anchor of the soul, both sure and steadfast, and which entereth into that within the veil; whither the forerunner is for us entered, even Jesus, made an high priest forever." "Neither by the blood of goats and calves, but by His own blood He entered in once into the holy place, having obtained eternal redemption for us." Hebrews 6:19, 20; 9:12. {GC 421.1}
For eighteen centuries this work of ministration continued in the first apartment of the sanctuary. The blood of Christ, pleaded in behalf of penitent believers, secured their pardon and acceptance with the Father, yet their sins still remained upon the books of record. As in the typical service there was a work of atonement at the close of the year, so before Christ's work for the redemption of men is completed there is a work of atonement for the removal of sin from the sanctuary. This is the service which began when the 2300 days ended. At that time, as foretold by Daniel the prophet, our High Priest entered the most holy, to perform the last division of His solemn work--to cleanse the sanctuary. {GC 421.2}
Notice that the sins were not cleansed yet but still "remained upon the books of record." The door to the most holy place was closed until 1844. (That date is calculated from Daniel 8:14, and the history behind it is very complicated, so I will leave it at that for now.) In 1844, the antitypical end-time Day of Atonement began, and Jesus as our High Priest moved from the heavenly holy place to the most holy place, where He began the work described by Ellen White in the first quote above, examining the record books in heaven and blotting out the confessed sins of professed believers, which had been transferred there via His blood, thus necessitating the cleansing of the heavenly sanctuary. That cleansing process continues to this day, having begun with an investigation of the lives of professed believers who had died, to make sure that all of their sins had been confessed so that they could actually be saved when Jesus returns, and then progressing to the professed believers who are currently living. The antitypical Day of Atonement will end when Jesus leaves the heavenly sanctuary to return to earth.
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Again, the above is a summary of the traditional Adventist doctrine, as taught by Ellen White. You will find Adventists today who hold to many different variations of it and some who don't even agree with it. I have many problems with the beliefs that I have described above, but in regard to the book of Hebrews, I believe that the Bible presents Jesus' work of cleansing as already completed at His ascension to heaven, signified by His sitting down at the right hand of the Father. One of the key texts is Hebrews 9:24-25. (Verse 24 is quoted by EGW above, as are several other verses from Hebrews, and I'm sure you'll notice also that she assumed, based on tradition, that Paul wrote Hebrews.). I'll quote those verses here, with a bit of surrounding context:
23 Therefore it was necessary for the copies of the things in the heavens to be cleansed with these, but the heavenly things themselves with better sacrifices than these.
24 For Christ did not enter a holy place made with hands, a mere copy of the true one, but into heaven itself, now to appear in the presence of God for us;
25 nor was it that He would offer Himself often, as the high priest enters the holy place year by year with blood that is not his own.
26 Otherwise, He would have needed to suffer often since the foundation of the world; but now once at the consummation of the ages He has been manifested to put away sin by the sacrifice of Himself.
27 And inasmuch as it is appointed for men to die once and after this comes judgment,
28 so Christ also, having been offered once to bear the sins of many, will appear a second time for salvation without reference to sin, to those who eagerly await Him.
The traditional Adventist teaching is that the context of those verses is not the Day of Atonement, when the high priest entered the most holy place. There's a whole argument about the Greek word used there and whether it means "holy place" or "most holy place" or "holy places." Really, the context is the determining factor, though, and I believe that the context clearly contains Day of Atonement references. What that means is that, according to those verses, Jesus fulfilled not only the sacrificial aspects of the OT ceremonies but also the high priest's Day of Atonement entrance into the most holy place with blood--His own blood, of course, rather than the blood of animals. His cleansing of sins was completed when He sat down at the right hand of the Father, long before 1844: "When He had made purification of sins, He sat down at the right hand of the Majesty on high" (Hebrews 1:3b).