What does it mean to play "positionally", and how do you train that? I often hear this term thrown around when people are analyzing chess, but I don't really know what it means. I assume it's a generic term that means to play defensively, or to set up for the future. If that's what it means, how do I learn when it's time to do that, and how to do that? If the meaning is more precise than that, what is it?
There are three general types of players: Positional, tactical, and universal, which is being adept and comfortable in both positional and tactical games. Tactical means that you love open positions that require a lot of calculation, and often include all-out attacks.

Positional chess is generally slower, and you work to build small advantages by placing your pieces and pawns on good squares. Using your pieces and pawns effectively, you gradually hope to create pressure and threats that force small (or large, if you are lucky) weaknesses in your opponent's position. Once you have one small advantage, you can often accumulate more small advantages, and with the accumulation of these small advantages, you hope to turn that into one big advantage with a final winning tactical maneuver, or "tactical shot".

I gave a very detailed list of positional elements in this post. Be aware that positional sense is one of the last things that a chess player develops, and it takes a lot of time to develop. Most players are pretty experienced by the time they really start to understand this well.