@helloimustbegoing
Yes, as jumba said, it's a tool to install Pale Moon. Extract the pminstaller-*.tar.bz2 and double click on the pminstaller.sh file. That's all you need to do. Here's a video of it:
http://youtu.be/2yzHBydyzgM . I did it through a local server and not the PM4Linux website because downloading 28MB archives only burns small holes in my pocket due to data caps, but it should give you an idea. Also, I did use the terminal (since I recorded it to find some bugs in the installer), but double clicking works as well.
Also, I would request you not to install via the method described by Night wing above. Yes, simple "extract and run" works, but installation tool is the preferred method unless there is some real reason why you cannot install it. For example, I can push distro specific fixes, when they arise, via the installation tool. If you don't use it, I'll have to write long articles about these things, and in the end everyone loses -- you'd think Linux is a poor OS and I'd get less downloads ("oh so complex to use").
Also, extensions and everything is installable in that mode. Similar to "Windows zip packed versions of Pale Moon", if that makes you feel better.
@Night wing
So you find extracting an archive and double clicking on a file to be similar to "trying to understand a foreign language"?
**speechless**
The command line are there for those who want to have more control over the installation. That doesn't mean that you have to use them, it's your discretion, but then again, please don't go on long rants on this subject. (BTW, I had to merge and shorten your posts. Please make your posts concise -- and I know you can do it.)