Tags provide a way for users (that means anyone who uses a website) to label things in a way that makes sense to them.
When you tag a question or answer, a restaurant or a bar on the main site, or even an event on the events calendar, you provide an easy way for like-minded individuals to find the item later.
You can visit the popular tags page to see what other members have been tagging things with.
For example, if you posted a question about kittens you might want to tag it "cute" so that other people in search of cuteness could easily find it later.
Tags are words, or sequences of words, with no spaces or other characters, like "cheapbeer," "spicyfood," or "foo".