Skype is proprietary software that allows you to make calls over the Internet using your computer. Skype uses decentralized peer-to-peer technologies, so your calls do not go through a central server, but through distributed servers and other users. It uses its own proprietary communication protocol to achieve this.
Since Ubuntu 10.04 (Lucid Lynx), Skype is part of the Canonical partner repository. To install Skype add the Canonical Partner Repository. You can do this by running the command
sudo add-apt-repository "deb http://archive.canonical.com/ $(lsb_release -sc) partner"
Then install Skype via the Software-Center or via the Terminal.
sudo apt-get update && sudo apt-get install skype
It is highly recommended to use the package provided in the Canonical partner repository, not the one distributed from the skype website, as the skype website currently points users to the wrong package for 64-bit systems of Ubuntu 11.10 and above.