Skydrive is basically cloud storage. You can use it to store pretty much anything and the standard storage space that you get for free is pretty decent. This means that you can store documents, photos, zip files, and music to the cloud and have it synced down to whatever device or computer you have attached to Skydrive. For example, on WP8 if you take a photo in the camera app the default behavior is to automatically sync that picture to Skydrive. If you have Skydrive installed on your computer and tied to the same account, that photo will show up in the Skydrive folder on your computer. Same thing with documents you create on the device. As far as music goes, you can sync it but as far as I know right now there is no way to play (stream) the music from Skydrive to your Windows Phone device. Hopefully this will be something that is included in the future, but for right now Skydrive is mainly for storage. One feature that I really like, is that Skydrive also has built in cloud office apps, so if you put a word doc into Skydrive you can open up your browser, go to skydrive and you can open the document and edit it just like you would in word.
In the end Skydrive is just Microsoft's version of cloud storage and is similar to what Google is doing with Drive and what Apple does with iCloud.
Also you don't need to be on wifi to use it, I use mine just fine on cellular. Although if you don't have LTE, you might have better syncing speeds if you're on wifi.