During the middle game chasing is a tactical method that you may use in order to capture a piece, particularly a queen. Chasing is just what the name implies, chasing a piece around the board that has limited movement options until you can safely capture that piece. The reason that this works the best in the middle game is because the middle game is when the board is often the most crowded thus limiting the movements of your opponent's primary pieces.
If you are chasing your opponents poorly guarded, or unguarded, queen around the board with say a bishop and a rook, you can continue to chase until your opponent either traps themselves into a corner or makes an error in their movement of that queen. You may choose to chase any piece around the board; the queen is simply a more significant capture. Chasing can also be utilized during the end game but may be a little more difficult since the board is generally less cluttered with pieces.
Chasing during the end game could be a good idea if your opponent has a rook and you have two knights or two bishops. Chasing this dangerous rook and ultimately capturing it will obviously help you in gaining a major advantage that will most likely lead to you placing your opponent into checkmate. Use the tactic of chasing wisely as you do not want to get so focused on it that you leave yourself overly exposed to attacks from your opponent. Sometimes people focus so much on the chase that they end up losing the pieces that they were using for the chase. Simply stay aware of all the options and look over the board before making a move to help avoid this blunder.