Distrowatch has decent information on the various distributions: http://distrowatch.com/
Also, hit-up the Wikipedia page for a specific distro if you want to learn more about it. There's usually some interesting information there.
The Linux Distro Timeline provides some interesting perspective as well: http://futurist.se/gldt/
You'll find major differences to be things like package management and software repositories, and minor differences may be things like configuration file locations, how to start/stop services, etc.
Others are just variants of a base distro that provide a preconfigured environment, enhancements, etc. For example, Ubuntu branches off of Debian, and Mint, Backtrack, and tons of others branch off of Ubuntu. Penetration testing distros like Backtrack provide a lot of preconfigured software and other customizations, while others, such as Kubuntu and Xubuntu primarily provide alternate desktop environments, such as KDE and XFCE, respectively. However, there's no reason you couldn't start with Ubuntu and end up in the exact same place yourself; it's just convenience. Check out the distro timeline to get a better idea of how everything is connected (note: Backtrack is erroneously listed as a Knoppix variant, which it was several versions ago; it is now based on Ubuntu).
To specifically address the others you mentioned, Mint is designed to provide an elegant experience, and Arch is a very minimal distro. You usually need to do a lot of manual configuration to get things working how you want, but it's great on systems with limited resources since you're only configuring what you specifically need.
Edit: had a work emergency between the time I started and submitted this post; good points, shadowzero
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