Someone who plays their notes with strength and power. Notes which sound full and round. This is not about having a loud amp, it is about digging into your notes to get your notes out of the bass with strength and confidence. This not only applies to bassplayers, guitarplayers should also dig into their strings to create a better sound.
Someone who is able to outline the structure of a song (playing the chordnotes) without the support of any rhythm instrument such as guitar or keyboards.
Someone who can create variations in feel of the song without altering or upsetting the tempo of the song.
Someone who can play the same feel, but vary their choice of notes, this to keep the song fresh.
Someone who can play supportive. Bassplaying is all about the support and feel of the music, it is not about being flashy. This does not mean bassplaying is boring and repetitive, no you can be as inventive when you play the bass as when you are when playing the guitar.
This list is by no means complete, the facts I mentioned here are only some of the main characteristics which make up a great bassplayer.