This is a traditional point-and-click adventure game with a twist (what else?). Basically, you play a character who doesn't know who they are and have absolutely no memory of the past at all. The point of the game is to figure this out, to remember, and that's where this gameplay mechanic comes in.
The game is broken up into both the current time and memories of the past. Memories are small self contained "episodes" that you can play through. You unlock memories by find things in the real world which trigger these memories. You can play a memory at any time, for whatever reason, and even go back and replay them. You'll want to do this because these memories are not complete.
Just having a memory to play doesn't mean you can "win" it just yet. Elements of the memory are missing, represented by television static. You can not interact with these objects until you remember what it is. In some cases, it might obviously be a dresser, but you don't remember what significance the dresser had, so you still can't see it. Even people may appear as television static, though you can talk to them in that form - you just might not have all the dialogue options available to you (gibberish random letters).
The way you "unlock" an object is by triggering a memory associated with it. For instance, you may find a key and remember that it came from that dresser. You could visit the same location in current time and trigger unlocks, though you could just as easily find that something fuzzy in your memory isn't there anymore. And, of course, winning a memory will undoubtedly unlock significant objects and story elements.
Unlocking an object will make that object available in all memories. So if you remember it in one memory, you can then go back to a previous memory and interact with it there too. It would be necessary to play many of the memories out of chronological sequence in an effort trigger previous memories.
Frankly, the concept is really very simple and interesting, but that is not enough by itself. A large part of the success of this idea will come from the plot and story structure. If things aren't written well, the entire swiss cheese memory concept would be more annoying than ingenious. But this is Three Hundred Gameplay Mechanics, not Three Hundred Ingenious Plots, so you'll have to just accept that the idea requires one heck of an implementation to work properly.