Mainly avoiding the round trip needed for each payload sent by the server, as mentioned in one of the other replies. It also avoids this issue with data sent by the client.

Note that these things can also be solved with HTTP by using streaming, so WebSocket isn't strictly required as a solution. About the only difference between two single-directional HTTP streams and a WebSocket is that the WebSocket ensures data in both directions travels the same network path, which may make scaling or stateful sessions easier to build.