As far as urban slang, the definition is "to show off." Used by many rappers, most notable Ice Cube and the Geto Boys. Originated in the urban community, and has been used for quite some time.
"...no flexin', didn't even look in the nearest direction as I ran the intersection. (This is said because Ice is trying to get away from some people who tried to kill him the other day In the song, of course)" -Ice Cube, "It Was a Good Day"
Term recently coined by Mos Def, now used freqently to describe the degeneration of hip-hop from an art form and expressive outlet to glorified criminalistic behavior and corporate domination of a once-underground phenomenon, i.e. De La Soul or KRS-One, who rap about every day events and important issues vs. 50 Cent or Juvenile (By-products of The Rape Over), who rap about murder, theft and what they buy with their millions of dollars (For example, 50 Cent's newest album is titled <i>The Massacre</i>).
"We over-do it add the fire and explosion to it/We're so confused so we run rap music
MTV is runnin this rap shit/Viacom is runnin this rap shit/AOL and Time Warner runnin this rap shit/We poke out the ashes for a chance to cash in
Cocaine, is runnin this rap shit/Hennessey, is runnin this rap shit..." -Mos Def, "The Rape Over"
The title of a Slick Rick song, the phrase was coined by Ricky D himself, used to describe the reluctance men should take toward women when getting involved with them. After the popularity of Rick's song with the same title, this phrase became popular.
"Treat her like a prostitute, don't treat the girly well until you're sure it's sweet." -Slick Rick, "Treat Her Like a Prostitute"