What kind of album are you trying to add the pictures to? You can only add items to standard albums you create yourself. It is not possible to add photos to albums in the "Library" section of the library, only albums in the My Albums section; and to add photos to Smart albums you have to modify the rules for the smart albums.
You can drag photos to Shared albums, but it may take a long time until you are seeing them in the shared album.
And you cannot "move" photos to an album, only "add" them to an album. When you add a photo from one album to another album, it will appear in both albums. The photos in the albums are not duplicates, just references. You can add a photo to many albums without creating duplicates.