Catch A Body is a slang term which means to kill someone. The term comes from the fact that once you kill someone, their body drops, and it's yours to deal with. This slang term is heavily used by Hip Hop artists in songs, though most of the time they're talking about friends and associates catching bodies, some of them have claimed to catch bodies themselves in songs.
The term 'Catch A Body' is sometime used metaphorically, for example, Cassidy had a diss song aimed at Meek Mill which was titled "Catch A Body (Meek Mill Diss)," the title of this song means that Cassidy is going to lyrically kill Meek Mill.
In Nas' "NY State Of Mind", Nas said ""N*ggaz be runnin through the block shootin
Time to start the revolution, catch a body head for Houston..." Nas is basically saying he's gonna start a revolution by killing one of the individuals shooting on his block, and then heading to a safe haven until things quiet down.
In Drake's "Headlines" song, Drake said "You know good and well that you don't want a problem like that - You gonna make someone around me catch a body like that." Drake is basically saying if you don't want to mess with him, if you do, someone around him is going to kill you. This is a perfect example of someone talking about catching bodies but ain't about that life, it's very unlikely that Drake even hang around people that are about that life.