Socket can have two meanings.
Noun
A socket is a placeholder for Gems, Runes and Jewels. These 3 kind of items won't have effects unless you place c.q. socket in the item. In the User Interface you will see grey circles. The number of grey circles on the item corresponds with the number of sockets it has.
Verb
Socketing is the act of placing socketable items (see above) in the item. You use the mouse to drag the Rune, Gem or Jewel you wish to socket to the item you want it to have.