Tag watching (formerly known as favorite tags) allows a user to select a set of tags on a Stack Exchange site. All questions with those tags are highlighted in the questions page. If a user is looking at a tag search page for a watched tag, the only questions highlighted will be those that have other watched tags.
There's a list of all watched tags in the preferences tab in the User Profile and on the right-hand side of every questions list page, along with an entry field to set them. They can also be set by hovering over the tag, and clicking on the "Watch tag" button. You can unwatch by clicking on the same button. You can also ignore certain tags by clicking on "Ignore tag". Questions with ignored tags can be set to hidden, or just faded out.
The watched/ignored tags are used by the Interesting Tab of the home page in Stack Overflow only as part of its algorithm to determine which questions to show.
This feature was originally called favorite tags, it was later renamed to tag watching or watched tags.
For more details see:
