Sockets are found on weapons, armor, jewelry etc. If an item is Socketed, then you can install Gems, which will benefit the object or the wearer of the object.
Sockets can be randomly added or removed by an Enchanter.
An item can have sockets up to the number of vertical spaces an item takes up in your inventory. (Ex: A Magic Staff 4 spaces high will allow up to 4 Sockets, while a Ring or Necklace will only have 1 Socket.)
Sockets increase the sale value of the item to a Trader.