MRP is role-playing that may involve violence, strong language, drama and quite often sex scenes, though unlike ERP, the scenes are a sub-product of the RP, not the whole RP.
MRP will usually be a long term role-play and anything that happens in the RP will effect the characters for the rest of the storyline. MRP is suggested only to those who can understand adult situations and consequences as well as those who do not mind having their character die or change completely if the RP calls for it.
MRP is basically RP that is rated R.
The term is often confused with ERP by people who think maturity means sex, but it is very different.