Assume you are asking a more general question than just what words 'DFRPG" stands for.
1
DFRPG is the commonly accepted abbreviation for the Dresden Files Role Playing Game
2
So what is a role playing game (normally abbreviated 'RPG')?
A subclass of games where you attempt to portray a specific character, and make decisions based on what that imaginary character might think or feel.
Wikipedia article3
More specifically, the DFRPG is what's normally called a 'table top' or 'pen and paper' RPG.
There are a few different sorts of RPGs floating around.
There are the big budget computer RPGS:
Big multiplayer ones like World of Warcraft or Everquest
Big single player ones like Dragon Age or Fallout: New Vegas
There are 'live' RPGs, where you dress up in costume
For example, various
SCA events
or more purely 'social' games, that don't involve hitting the other players with padded weapons
like the live action version of Vampire, published by White Wolf Games.
Then, there are the 'pen and paper' version which are (mostly) played by people sitting around a table, talking, rolling dice, making marks on paper, and eating cheetos.