Email or private messages are fine for traditional "penpal" sort of communications (i.e. writing out letters of a couple of paragraphs and awaiting a reply), but much less so for real-time communication, or "chatting". This can be either written or spoken.
Probably the most useful aspect of Skype for language learners is voice chat. If you have a microphone on your computer, you can have the equivalent of a phone call to anywhere in the world for no cost (as long as the other person has their own computer and microphone.) You can also make calls to phones from Skype - they do cost money but it's very cheap.
(I sound like I'm pimping this product now, lol. I'm not, honestly! They don't pay me! (wish they did...))