Jeez. From the help section:
Long Relief A/B - Long relief pitchers are the first to come in when the starting pitcher is removed early (generally before the 7th) in a game that is still in doubt. These are usually relief pitchers who are capable of pitching multiple innings of relief at maximum effectiveness. Unless settings in the Edit Players Settings page dictate otherwise, the long relief A pitcher will be given first priority to enter a game when this situation arises and the score is still close. If there is a wide margin in the score your long relief B pitcher will have a better chance of appearing in the game. If a long relief pitcher must leave the game during what is still a long relief situation, first replacement priority will be given to another long relief pitcher. For reference, these are also often times spot starters for teams in case of injury.
Setup A/B - Setup relief pitchers are the first to come in when a pitcher is removed late (generally during the 7th or later) in a game that is still in doubt. These are usually relief pitchers who are only capable of pitching an inning of relief at maximum effectiveness. Their appearances are usually higher than any other pitching role, while they may not pitch as many total innings as starters or long relief pitchers. Unless settings in the Edit Players Settings page dictate otherwise, the setup A pitcher will be given first priority to enter a game when this situation arises and the score is still close. If there is a wide margin in the score your setup B pitcher will have a better chance of appearing in the game. If a setup pitcher must leave the game during what is still a setup relief situation, first replacement priority will be given to another setup relief pitcher. Setup pitchers are intended to bridge the gap from starters to closers.
LH/RH Specialist - Specialists have become quite common in baseball. These are pitchers who are almost solely used just to get the opposing team's most feared hitter out late in a close game. For example, a -handed specialist will enter the game to face the opponent's best -handed hitter (and vice versa).
Mopup - The mop up setting is used to designate a pitcher to be used in blowouts (either winning or losing). Blowout is determined by the deficit (or lead) and the inning, e.g. an 8 run deficit in the 2nd inning would not be considered a blowout, but the same deficit in the 8th inning would be. Mop up designated pitchers could possibly be used in non-mop up situations. They will always be used before pitchers marked as 'rest'. For example, if you have 5 relievers and 1 is marked as rest, 1 is marked as mop up, 1 is marked as long relief, 1 is marked as setup and the last as your closer, and your game went to extra innings, if your closer, setup, and long relief had already been used, then your mop up pitcher would see action.
Closer A/B - Closers come in when a pitcher is removed late (generally during the 8th or later) in a game that is still very much in doubt. These are usually relief pitchers who are only capable of pitching an inning of relief at maximum effectiveness. They are also usually the best relief pitchers on a staff. Unless settings in the Edit Players Settings page dictate otherwise, the closer A pitcher will be given first priority to enter a game when this situation arises. If a closer must leave the game during what is still a save situation, first replacement priority will be given to another closer relief pitcher. Closers are supposed to seal victory for teams in close games.