Socket bayonets are characterised with a metal sleeve (the socket) that are used to attach the bayonet to the gun.
The socket bayonets was the next level in development after the plug bayonet. For the socket bayonet, the blade was placed a bit to the side of the weapon allowing the gun to be reloaded and fired with the bayonet mounted. The socket bayonet was not nice to hold when it was not mounted on the musket and they were not suitable to use as a sword or knife. This lead to the development of other types of bayonets. Sometimes we see use of socket bayonets in recent times. One example is the British L3A1 (SA80) bayonet.