Socket can have two meanings. Generally, sockets refer to 'holes' in items that can be used to insert special other item in those, thereby adding their properties to the properties of the item that has sockets. Socketing (or to socket) refers to the process of performing the named action.
A socketable item means both an item that has sockets, and an item that can be inserted into a socket.
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. Each socket may only hold one socketable item.
The number of sockets per item type is limited (up to 6 in Diablo II and up to 3 in Diablo III). In Diablo II, the maximum number of sockets depends on the level of the monster that dropped the item: most of the time, up to 3 sockets at Normal, up to 5 at Nightmare and up to 6 at Hell.
The sockets are a way of customizing your gear, putting the bonuses of your choice. Many socketable items change their effect depending on what item type they are socketed into (weapon, armor, helm, off-handed item). Runes are a special type, as they can form Rune Words if socketed into a proper item in the correct order.
Types of socketable items (numbers in brackers show maximum number of sockets possible):
- Diablo II: Weapon (6), Chest Armor (6), Shield (6), Helm (3) (all grant different effects from same gems and, sometimes, runes), note that these limits, while seen possible by the game engine, are very hard to get to.
- Diablo III: Weapons (1), Armor (Chest Armor 3, Pants 2, Shield 1, Off-Hand item 1, Amulet 1, Rings 1 each), Helms (1), total of 10.
Once the item is socketed, it may be unsocketed (i.e. the gem, jewel or rune may be extracted, leaving the socket vacant for a new socketable item). In Diablo II, you will need to use a Horadric Cube, losing the old gem (rune, jewel) in the process. In Diablo III, you can use the Jeweler's service, which will clear the sockets and return gems to you, for a fee, price depending on the quality of the gem(s). Alternatively, you may salvage the item, which will return the socketed gems to you for free (but will destroy the item).
Having socket(s) counts as one affix for an item (always one property, regardless of the number of gems). In Diablo III, it is always a Primary property.
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. Socketing does not require any special actions, but unsocketing (see above) does.