(I may have gone overboard here, but in my defense this post is tagged in the Lore category)
Desmond's Journey has 5 parts to it, it's base game content. You need to find more data fragments to unlock the later sections. The premise is that Desmond is interfacing directly with the Animus' genetic memory reading routines, but instead of viewing his ancestor's memories he is viewing his own memories and piecing his mind back together. The point is to use the building blocks you have to navigate through each section of the world as Desmond is crawling around inside the Animus' raw computer coding. It's pretty easy.
The Lost Archive DLC is the same mini-game as Desmond's Journey but greatly expanded and much more difficult. It's a cool diversion and gives you some insight into Clay's (Subject 16) history and exactly what he's been doing while he is stuck in the Animus, but I personally don't like it that much gameplay wise.
(Minor spoilers for Assassin's Creed 2 ahead)
(No real spoilers for Lost Archive)
The Lost Archive follows Clay in the time frame immediately after Desmond found all 20 original data fragments Clay left behind, but before finding all the fragments in Brotherhood. At this point in time, Clay (not true Clay, an A.I program he created using the Animus' scans of his brainwaves) has been pieced back together by the data fragments Desmond found, but was then immediately trapped inside the Animus archives because the Animus thought he was a foreign program or virus and quarantined him. You have to continue replaying it on a loop until you find all the data fragments in the Lost Archive and locate the hidden backdoor to escape the quarantine.
(Lost Archive content ends here)
(Clay's entire story after Lost Archive up ahead if you're interested)
(Minor spoilers for Brotherhood)
That's where the DLC ends, but chronologically Clay escapes the Lost Archive and piggybacks on the Animus' Virtual Reality Training Program and become a sub-routine of that program so that the Animus does not isolate and quarantine him again. Before he died, Clay had also left 10 more data fragments throughout the Animus where he knew Desmond would be able to find them because he knew the memories the Assassin's and Templars were after, those are the data fragments in Brotherhood. The Brotherhood data fragments are quarantined by the Animus because the Animus does not know what they are or where they came from, that's why they have to be decoded. From what I gather when I decoded them all, the fragments were supposed to do two things: tell the subject who found all of the fragments that Clay (or part of him) was still alive, and once all decoded input a command to transfer Desmond to the file he was hiding in the VR program where he has the ability to materialize himself in a way that Desmond is able to comprehend. (As a foreign program, Clay did not have free reign over the Animus, he had to hide within programs or risk being isolated and quarantined. If Clay had tried to hide anywhere else, then he would not have been able to attempt to use the Animus' character fabrication program and make contact with Desmond without being detected as a foreign program and quarantined again, and Rebecca did not notice him in the VR program because he was hiding from the Animus' system scans by pretending to be a sub-routine, otherwise he would have tried to make contact with Desmond sooner - at least that's my theory)
(All spoilers end here)
Then in Revelations Clay leaves the safety of the programs he was hiding in to join Desmond in the Animus safe room, where Desmond is now able to see and hear him because the safe room is made up of raw simulation data, so Clay being a program is able to interface with the character fabrication resources at will here. He then uses his prior knowledge of the quarantine system to distract the Animus so that it does not try to delete or quarantine Desmond when he leaves the safe room to view Ezio's memories. And if you don't know how it ends, you'll find out as you play the game. There is nothing left for me to cover.
At least that's how I interpreted all of it, and the Lost Archive DLC pretty much confirmed my theory in my opinion. So if anybody read this far, what do you think?