Nothing is stored in Gallery, since Gallery is just an app - there's no "place" to store anything for it (no data folder).
When you start (or restart) an Android phone, Media Scanner scans all of storage, internal and external, for media files - sound files, video files, picture files, and builds a database. Gallery looks in that database for any picture or video files and shows them. Each folder that has a file being shown is shown as a separate "album" in Gallery.
Get a file manager like
Total Commander, so you can have 2 folders open at once (you have to turn the phone to landscape mode) and you can move your pictures to different folders, make new folders, etc. Maybe fiolder named "My Pictures", then folders in that like "Beach", "12-25-14 Party", etc., and put the picture files into the appropriate folders. (Copy, don't move. If the copy was successful, delete the original. If a move blows in the middle you can lose the picture.) Now Gallery will show you albums like Beach, 12-25-14 Party, etc.