What does consolidate do?

Here's what "consolidate" does (from iTunes' help):

HideConsolidate your files in the iTunes folder

Depending on how you imported items into iTunes, some items in your library might be stored in different locations (in another folder or on another hard disk, for example).

You can consolidate all the files in your library in the iTunes folder—for example, to make it easier to move your library to a new computer.

1. Choose File > Library > Organize Library.
2. Select “Consolidate files.”Files remain in their original locations, and copies are placed in the iTunes folder.
3. To create folders (Music, Movies, TV Shows, Podcasts, Audiobooks, and so on) inside your iTunes folder, and place all your imported media files in the appropriate folders, select “Reorganize files in the folder ‘iTunes Media.’”

What about duplicates? I recently downloaded some movies from iTunes and ended up with double copies (and with "show iTunes in the cloud" turned off). Will consolidation remove the extra copies?

No. The Consolidate function works as described above - it copies media files that are referenced in your iTunes Library and are not in the canonical iTunes Media folder structure into that structure. It does not address any issues of duplicates. There are, however, multiple threads here addressing this topic (most recently Duplicate Tunes).