Project is where you store photos to during import. For instance, "Vacation in Hawaii" project.
Albums is like photo albums on your bookshelf. You can assign photos from one or more projects into albums. For instance, "Maui" album.
Folder lets you group multiple folders, projects, and/or albums together. For instance, "2008" folder.
Expanding you have:
- "2007", "2008", etc. folders at the top level
On "2008" folder, you might have "Vacation in Hawaii" project (among other projects) and perhaps "Best of 2008" album.
On "Vacation in Hawaii" project, you might have "Maui", "Big Island" albums.
"Best of 2008" album will have your favorite photos from various projects shot in 2008.
iTunes to Aperture analogy:
Song:Album

laylist:Folder = Photo

roject:Album:Folder