It seems to be incredibly slow which kind of defeats the purpose of having a text-based browser to begin with. I'm not sure, but it looks like it's taking the output of a headless Firefox and turning it into ascii. If that's the case I'd rather stick with something like Lynx, etc.
The point is when you have a connection with limited bandwidth. In such cases you can host browsh in the cloud and connect to it with ssh/mosh. You get a much better experience than text based browsers at a limited bandwidth. It's great for such cases - I use it when hiking / working away from good internet.
https://news.ycombinator.com/item?id=25132746
The main use case for this is when you want to experience a browser in a terminal, including if you don't have X or a GUI setup.