Here is a screenshot:
On Math.SE, the yellow highlighting denotes that you are "watching" a tag. In the above picture, I am watching measure-theory. This is also indicated by the eye symbol.
There are a few ways I know of to watch a tag. One of them is prone to misclicks: simply mouse-over a tag you want to watch, then at the bottom of the tooltip, click on "watch tag".
If you are already watching the tag, there is an "Unwatch" button instead.
These buttons also appear on the page that you get after clicking on a tag:
The other way is with the "edit" button in the top-right of the list of Watched tags on the right of the front page. After clicking, you should type in the tag you want to watch, or click on the $\otimes$ to unwatch.
Note that the eye doesn't appear when there are too many tags, or the tag is too long. There is also the option to 'ignore', which greys out the question and displays a crossed out eye . These can be seen in this screenshot. Ignored tags can also be edited in the corresponding list on the right.