I’m travelling around the world and sometimes I don’t have very good Internet. If all I have is a 3kbps connection tethered from my phone then it’s good to SSH into my server and browse the web through elinks. That way my server downloads the web pages and uses the limited bandwidth of my SSH connection to display the result. But it lacks JS support and all that other modern HTML5 goodness. Texttop is simply a way to have the power of a remote server running a desktop, but interfaced through the simplicity of a terminal and very low bandwidth.
Why not VNC? Well VNC is certainly one solution but it doesn’t quite have the same ability to deal with extremely bad Internet. Texttop uses MoSH to further reduce the bandwidth and stability requirements of the connection. Mosh offers features like automatic reconnection of dropped connections and diff-only screen updates. Also, other than SSH or MoSH, Texttop doesn’t require a client like VNC. But of course another big reason for Texttop is that it’s just very cool geekery.