VGA Planets is a client/server game. The part which you as a player will most likely talk to is the client program. There are quite a number of clients available. See also the relevant glossary entry. The server program is often called host in the VGAP universe.
The client program displays your empire graphically, and lets you enter your moves. For example, you can tell a ship to move to a particular planet. This is just an order, the ship will not yet start moving. You can at any time cancel that order. If you tell your ship to rob someone, you'll not immediately get their stuff - you don't even know what they have.
When you are done with your turn, you compile a turn file and send that to your game master. He'll use the server program (which is probably PHost) to generate new result files. Here, the ship will actually move and rob, and the server (or host) program will tell you what happened.
Some orders, however, are already processed by the client. When you transfer cargo between two of your units, that will be immediately be performed.
The rule is simple: if you know all details of the participating units, there's nothing which could go wrong, so the order is executed immediately. All other orders are processed host-side.
Play-by-Email (PbEM): Traditionally, you send your turn file to the host using email, and receive your result file by email as well, which makes VGA Planets a Play-by-Email game. Today, many hosts also have a WWW turn upload function.