Linux, more than anything else, gives you choices. There are hundreds of distributions, many desktop environments, and a near infinite variety of ways to set up your system. Some distributions give you a slick installer and a fully configured system right out of the box, other distros require more work to set up. Arch Linux is the later. So why do I choose to run it?
The base Arch Linux installation contains only the minimum necessary packages to boot into a terminal on a working system. It comes with no desktop environment, no printer, bluetooth, or audio drivers, no network connectivity packages, very few utilities, and no user-space applications. It makes zero assumptions as to what any particular user might need, allowing them to build exactly the system they want, with nothing they don't.
Because of its minimalism, Arch demands that you become a competent system administrator. Arch does nothing for you. You have to roll up your sleeves, install and set up the base system from the command line, and install and configure every detail of the entire system to your liking. To develop enough skill to do that takes a lot of time and effort. You will learn a lot building an Arch system. And when you're done, you will not only understand your system far more deeply, you will feel much more connected to it.
With Arch, there is no "version". You are always running the latest packages. Many distros have stable, slow release cycles, which makes an update something you perform every year or two. An update can be a big event--a scary one, even, since so much changes in one fell swoop. With Arch, updates are available every single day, and as long as you stay current, if something does break, it's pretty easy to identify the problem and fix it. And if you really want to be on the bleeding edge you can enable the testing and unstable repos.
Arch has an excellent, well regarded package management system, along with some of the largest, most up-to-date repositories. I have yet to find anything I needed that wasn't available in either the official Arch repos, or the AUR. And when a new package version is released by a developer, it's usually added to the Arch repositories very quickly.