Yes, you're right!
They are the ones responsible for signing and "coaching" artists.
They decide what an artist relese, and how they do it etc...
Of course it's different from label to label but on the major labels the a&r has the final word on everything an artist does!
E.g. what song is going to be the single, what producer is gonna' do the track etc.
Hope I cleared something up...
PEACE!