It makes the connection appear completely lagless, since the Mosh client echos typed characters locally instead of waiting for a round-trip with the server.

It also buffers all command output server-side and doesn't send more output than the network connection allows. This means that even if you have a runaway process dumping lots of output, you can still immediately Ctrl+C it.

You can do that with client-side rlwrap too.

Auto-reconnect is another advantage.