Web sockets make it cheaper to talk to your servers.
Connecting to a server takes some time, so with web sockets, you make that connection once and then keep using. The major benefits of this are:
It is faster to send messages. No need to do a bunch of work for every single message.
The server can push messages to you. With normal HTTP you would have to keep asking for changes, but a web socket, the server can talk to you whenever it wants. This means there is less unnecessary network traffic.