In the distant past, Skype messages were encrypted and were considered secure and private. But lately there’s been growing evidence that they are no longer private. It seems that Microsoft (the new owners of Skype) have been monitoring messages.
Ars Technica did an experiment by sending a unique link. They monitored their server logs and found that someone (or some system) at Microsoft accessed the link. In less technical terms, this is proof that that Microsoft have full access to your Skype messages. Details of the experiment are here.
Also, another company called H-Online recently did a similar experiment and came to the same conclusion.
This isn’t a risk for most people, it’s just something to be mindful of. Especially if your work requires privacy.