Depending on your band's viewpoint, it can mean almost anything.
U2 and Coldplay for example list each member of the band as the songwriters. This was an agreement between them to avoid any of the publishing royalty arguments that bands like the Beatles had.
I think if you are contributing something of your own composition to a song, then you are a songwriter. Hard for a drummer, I guess, if all he is doing is providing a standard 4/4 beat. Something like that can't really be copyrighted.