Microsoft has been talking about Skype for Web, its plan to allow users to talk with their friends without installing Skype on their computers, but the actual solution hasn't seen the light of day. Until now.
Microsoft has begun a private beta program for Skype for Web, a way of bringing the Skype VoIP service to a Web browser without requiring users to install the client software on their devices. Microsoft first announced Skype for Web in November.
Ideally, this would be more beneficial to people using hardware that doesn't have a native Skype client than for PC users, where the software exists. You can log into Skype.com now, but all you have access to is your account information. Eventually, the chat, voice, and video features will show up.
There don't appear to be any major differences between regular Skype and Skype for Web, except that the Mac version of Chrome doesn't support voice and video calling, so Skype for Web won't work on that platform. Other than that, the basic features of chat via text messages and sending/receiving voice and video calls is intact.
For now, Skype for Web is a closed, invite-only beta test. It will likely open up in a few months. It supports Internet Explorer, Firefox, Chrome, and Safari.