Pocket speed is just enough to get the ball to drop in the hole without hitting the back of the pocket.
It's a good reference point when you're talking about speed control, but isn't used all that often in most games (one pocket being the main exception).
The possible advantages of shooting a ball at pocket speed are:
-It makes the pockets play a little bigger. Clipping the near rail of a corner pocket at high speeds imparts spin on the OB that can cause it to rattle out; on a slow shot, that effect is greatly reduced.
-It leaves missed balls hanging in front of the pocket. This can be useful in games where you and your opponent are playing different balls (8-ball) or different pockets (one pocket).
-It creates more swerve, cut-induced throw, and spin-induced throw. I could have listed these separately, but they all fall into the category of effects that are more pronounced at low speeds. Knowing this allows for some shots that just aren't possible at high speeds.
The possible disadvantages of shooting pocket speed are:
-Inability to play position. English, draw, and follow effects all vary significantly with speed, and some position routes are longer than others. It's pretty rare that the best position play can be achieved with a pocket speed shot, especially in rotation games.
-More susceptibility to table roll. The worse shape the table is in, the more of a problem this is, thus the tendency for bar box players to fire balls in.
-More swerve, cut-induced throw, and spin-induced throw. As mentioned above, sometimes this can work in your favor, but it is usually just adding additional complications that have to be compensated for.