"Heavy RP" means that you'll be often "locked" into that character while in game. You don't do a lot of game strategy or OOC talk, you talk as a full character in the world with any tactics are done in character. Anything that happens with your hero, happens to your hero. You'll often have a bio and character listing somewhere, but that's not required for Heavy RP.
It's not "Oh, sorry guys, I got pk'd. Respawning."
It's "that sleemo jumped me in that back alley. Did anyone see that?"