A middle reliever is a relief pitcher who is used to pitch in the "middle" innings, usually the 6th or 7th inning. Although those innings are actually after the halfway point of the game, they are considered to be the middle of the game for pitching purposes because they span the space between the starting pitcher and the closer.
In practice, middle relief has never been very clearly defined as a role. Instead it's used as a catch-all for any relief role that isn't defined as something else. Because there is no such thing as a stereotypical middle relief role, there is also no stereotype of a middle reliever. On a team with an excellent bullpen, the middle relievers may be pitchers who would be used as setup men or closers on other teams. On a team with a weak bullpen, the middle relievers may be whatever warm bodies the general manager was able to scrape up the past off-season.