Space stations can be a big part of No Man's Sky. There is one or two space stations in every solar system.
Trading
One of the things you can do in space stations is trade with the people there. You can trade any resources for currency or buy something else from them.
Buying
The currency in No Man's Sky is important. Although you can get resources and items on planets. You might also find that you can buy resources too. In the space stations your also able to find ships. Without a ship in a game like this, your pretty much stuck on the planet your on.
Destroying
You actually can destroy the space stations, but it is so incredibly hard you'll almost never be able to do it. Although the outcome of destroying on of these space stations is unknown. We can only assume the reward is huge. Destroying one of the space stations could also cause a space battle.