Once you sign up for a Wikipedia user account, you'll receive occasional notifications of on-site activity. These work very much like Facebook notifications, but you'll never see one about new friend requests. Wikipedia has two types of notifications found in the top links on any page.
At left is Alerts, represented by a bell icon, which show up when your username has been mentioned by someone on a different page, someone thanks you for an edit, and also for a few other typically less common events.
At right is Messages, represented by a speech balloon icon, which shows up when there is a message on your user talk page.
Notifications are a relatively recent feature on Wikipedia. To learn more, check out the Wikimedia blog post from the 2013 announcement. Of course, if you don't want to receive them at all, notifications can be turned off in Preferences.