Here are some of the key features:
* Very quiet
* Beautiful OS (Linux based), very easy to use
* Account manager: Very easy to use with multiple settings (bandwith, disk space, programm rights, administration rights, group management etc)
* Cloud server function: Sync files between PC's and / or phones
* Backup function: Windows, Mac
* iTunes server
* Music server and player: In my opinion better an iTunes. iOS, Android and Windows Phone app available
* Video station: Movie management, IMBD support (works really great)
* Photo station: Photo mangement tool
* App store: Get more programms for it from Synology or other developers
etc etc etc
I could go on for hours I have this NAS for half a year now, and I've done a lot of research before I bought it - I'm more than happy with what I got. In my opinion, the biggest plus with the Synology NAS is how easy it is to use.
If you have any questions about the Synology NAS, don't hesitate to ask
Price - I don't know how much it costs where you live, but here in Switzerland, it was one of the cheaper ones.
The 112 will be fine, but if you want to extend your storage, I would go for the 212j - you get it for the same price as the 112. It has a less powerful CPU, but you have two hard drive bays. Synology 212J Compatible hard drives
If you already know that you will never use more than two hard drive bays, you can go for the 112 and just plug some external hard drives in over the USB...
I always used Synology, there are cheaper ones out there, but I never used one. I don't know if you will need all the functions Synology offers. Is there somebody at Tomshardware who has experience with cheaper NAS?
NAS: It is a network storage. So you hock it up to your router or switch, and Synology f.e. automaticly gives you a DNS. This way, you can access your storage and the full OS over the internet over the web adress of your choice. You can also access it over your local intranet (Internet at home) of course. Look at some of the reviews of Synology on Youtube, you will see how it works.