Socketed items arrived with The Burning Crusade. In a nutshell, these items are just like any other item in World of Warcraft but with one exception. They can be upgraded by socketing magical gemstones into the items themselves.

While some players are kind of doubtful if they are worth the trouble, Blizzard Entertainment believes otherwise.

According to Blizzard, the number of sockets and the specific types of gems used will allow for a variety of customizations depending on how a player wishes to improve the character. If partnered correctly, socketed items can be likened to an enchantment.

The official WoW site has a dedicated section for this topic. There are a lot of FAQs there and tips that will prove to be useful for players. One good example to share is as follows:

What can you put into a socketed item?

There are three primary colors of gems that can be placed into a socketed item: red, blue, and yellow. In addition, there are "secondary colored" gems - orange, purple, and green - that match two colors. Players can place any color gem into a socket; however, matching all of an item's sockets with their corresponding colored gems can award additional bonuses. These dormant bonuses appear in grey text below the sockets. There is also a special type of gem called a meta gem, which fits specifically into a meta gem socket.