This is a mailto link, and it will cause your browser to attempt to open your default mail program. It works automatically on most smart-phones set up with a mail client, or a computer properly set up with an email client program. If you do not want to use it this way, you can right-click on the link and select the option to copy the e-mail address and paste it into the "to" field in whichever e-mail method you use.
If you do want to use the nifty "mailto" link, you'll need to have an e-mail client configured to use it. Your e-mail client has to be configured with the correct server address, port address, and protocol to access your e-mail account. The information is specific to the e-mail service you use, for example: Hotmail, Yahoo! Mail, AOL Mail, or GMail. The MozillaZine Knowledge Base has information for connecting most e-mail services to Thunderbird and other mail clients.
If you want to use e-mail, it can be difficult to think of a likely, free, reputable provider that isn't attached to a massive markiting machine. The following are some good email providers that I have found:
A link beginning with "xmpp:" will attempt to open your chat application, if your browser supports the URI link. I don't know a reliable way of configuring a browser to do it, but if I figure it out I will write about it here. In the mean-time, just add me via your Jabber/XMPP client using the address I've supplied on my profile page.
Jabber/XMPP is a standardized, federated instant messaging (and presence) protocol that facilitates instant text communication between many different domains on the internet, much like email does for formal letter communication. If you want to use Jabber, go to xmpp.net, choose an XMPP server, and register for an account. You'll probably need to download and set up an XMPP client like Pidgin for PC or Xabber for Android, then you can communicate instantly with other Jabber users.