Arch has no specific "Arch things" to show off. With the exception of the package manager and AUR there really isn't much to it, and pacman and AUR are.. pretty basic as well and not the most user oriented programs out there.
That said, although its not the best in some areas, id say the lack of toying with things is a cool thing to show off. Packages closely align with upstream, you get what you should expect when you install something.
Explaining the concept of rolling release and its benefits would be good. A lot of people think rolling release isn't stable and that stable means Debian stable. But in reality rolling release doesnt use unstable software it uses fully released packages from the developers who made them.
Arch isn't the best at rolling release, not due to unstable packages, but due to the lack of tools to inform users of any changes that may break the system, but this isnt something that affects just rolling release distros if affects all distros, Arch just isn't the best at handling it. (they only inform you on there website)
Rolling release (and an extra repo) means you can have something like this (below) easily, without pains of package conflicts or breakages or incompatibility with ancient (in free software terms) software:
[a@jupiter ~]$ glxinfo | grep OpenGL
OpenGL vendor string: X.Org
OpenGL renderer string: Gallium 0.4 on AMD PITCAIRN (DRM 2.42.0, LLVM 3.8.0)
OpenGL core profile version string: 4.1 (Core Profile) Mesa 11.0.0-devel (git-42d283a)
For context, this is me running the latest AMD Mesa drivers giving me full OpenGL 4.1 support on the free software drivers rather than the propitiatory AMD drivers (its nice :D)
I added the mesa-git repo and pulled the mesagit group package, that was it.
/etc/pacman.conf
[mesa-git]
SigLevel = Never
Server = http://pkgbuild.com/~lcarlier/$repo/$arch
Now i can play more games without worrying about binary drivers.
(speaking of repos, for KDE people, the kde-unstable repo will give you the latest KDE :D it works really well. (you need testing too))
[kde-unstable]
Include = /etc/pacman.d/mirrorlist
[testing]
Include = /etc/pacman.d/mirrorlist
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Arch (and similar distros like Gentoo/Funtoo) is a make what you want of it distro. Theres no silly gnome spin, kde spin, cinnamon spin, etc etc etc. Something I really hate especially when i see people wanting to try a different DE and thinking they need to use Kbuntu or ubuntu gnome, etc. Its a bad misconception, and isn't something that used to be common, It used to be that you would download your distro and when you went to install it it would give you a choice of desktop environments.
Arch on the other hand doesnt give you that perceived restriction. You can install whatever you like. This is good. :)
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Speaking of the installation.
The cool thing about Arch (and this is common among the make it how you like distros like Gentoo) is you can have a fully functional system very quickly.
People are a little daunted by meeting a black TTY terminal, and for your grandma sure, that's maybe not ideal (though thinking about it.. its super simple, maybe it is a good idea...), but the blank TTY is the base of your OS that you can now customize to fit exactly what you want.
Another thing when it comes to installation is the wiki. Its pretty good and the installation guide is pretty good to. Though id say that the installation guide can be a little hard to follow, if you take your time with it it does cover everything you need.
Once installed and rebooted, systemd is your friend, it has good system admin utilities (which is great because as mentioned Arch never really had any). Things like timedatectl, localectl, hostnamectl are all really useful to get your system setup properly. Although these wont work as expected when initially installing (not sure why, maybe the chroot or simply because the system isn't in a usable state yet), you can use them to finish off your initial config.
For example, need NTP setup? you can use one of the usual NTP clients out there or just run timedatectl set-ntp on
localectl is also really useful for getting your system to have the correct locale across all parts of the system
I suppose that's not really Arch specific though (thinking about it, a systemd video showing how some of these tools works and using unit files and systemctl might be a very useful idea, i don't think there's a good guide to show exactly what systemd can do you for)
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Back to Arch. The AUR is quite good, and the fact is, at some point your going to have to use it. the main repo simply doesnt have enough package. Ive never had an Arch system where i havent eventually had to use it for something.
AUR is good, its easy to use but its basic, and its a little hard to manage mainly because the Arch devs will not integrate it in any way into the system or pacman.
Its somewhat like Gentoos ebuild system, except Gentoos is a bit better integrated. It means you can if you wanted to add your own packages by making a PKGBUILD and adding it to AUR.
The AUR also has most of everything you might need that the main repo doesnt. But to make the most of it and actually be able to manage it you need a 3rd party aur helper. Theres a lot out there. I really like aura but the current version occasionally cant resolve dependencies, I also use packer which works very well.
edit: it seems i started to answer your question and went off a little, hope its useful information.