It's called BASH is Born-Again SHell. Get it? It's like the normal shell, but more powerful. For example you can customize it (though you don't need to) through a text file at /etc/bash.bashrc. My favorite enhancement is the use of the D-pad to navigate through entered text.
It doesn't run like a normal app. It's a replacement for the commandline shell.
To use it, launch your favorite terminal apk, for example ConnectBot or Android Terminal Emulator and enter: