No, it is installed. This is not a program that you launch. This is a program that aids in SSH'ing things to your phone. That is a short term way of saying it, I am not going to get into specifics. Install OpenSSH now. Now you can use Terminal and add things to your phone an easy way.
The BSD subsystem adds commands that are not on the iPhone from the factory. These commands work with many of the 3rd party applications that you can download. All of these commands are the usual command line commands like cp, mv, mkdir, chmod etc.
Mobile terminal allows you to work with the command line on the iPhone. If you are not familiar with the command line for unix/linux, then it is probably best that you do not download the application. If you are the type to poke around and learn, then it could be something to have.