Socketing is the process of embedding a rune into the available slot in your weapon. An empty rune socket looks like this: . Please see the relevant runes page to find what upgrade is best for your build.
Weapons and armor may have up to three sockets. There is no cost for socketing an empty slot although you must be at the crafter
You can remove a socketed rune and save it in your inventory, and thus you can place a new rune on a socketed weapon.