If you only have a 3kbps internet connection tethered from a phone, then it's good to SSH into a server and browse the web through, say, elinks. That way the server downloads the web pages and uses the limited bandwidth of an SSH connection to display the result. However, traditional text-based browsers lack JS and all other modern HTML5 support. Browsh is different in that it's backed by a real browser, namely headless Firefox, to create a purely text-based version of web pages and web apps. These can be easily rendered in a terminal or indeed, ironically, in another browser. Do note that currently the browser client doesn't have feature parity with the terminal client.
