Wikipedia has a good explanation of tags and how they work.
A tag is a non-hierarchical keyword or term assigned to a piece of information (such as an internet bookmark, digital image, or computer file). This kind of metadata helps describe an item and allows it to be found again by browsing or searching. Tags are chosen informally and personally by the item's creator or by its viewer, depending on the system. On a website in which many users tag many items, this collection of tags becomes a folksonomy.
What's folksonomy? Folksonomy (also known as collaborative tagging, social classification, social indexing, and social tagging) is the practice and method of collaboratively creating and managing tags to annotate and categorize content. In contrast to traditional subject indexing, metadata is generated not only by experts but also by creators and consumers of the content. Usually, freely chosen keywords are used instead of a controlled vocabulary. Folksonomy is a portmanteau of the words folk and taxonomy, hence a folksonomy is a user generated taxonomy.
Here's an example from Wikipedia:
A web page hosted on a web server or blog server which supports tagging might have the tags "Baseball", "Yankees", "Tickets", "Away Games", and "Discounts". A human reader can probably tell the purpose of the page by quickly scanning the list of tags. Typically, the server displays the tags in a list on that page, with each tag displayed as a web link leading to an index page listing all web pages that use the tag. This allows a reader to locate quickly all pages which have been associated with the term Yankees. If the server supports tag searching, a reader would be able to find all pages that use a particular set of tags, such as "Yankees" and "Tickets".
If the page's author wishes to reclassify the page, they need only change the list of tags. In this case, the author could add the tags "Blue Jays" and "Paypal" to their page. All connections between pages are automatically tracked and updated by the server software; there is no need to relocate the page within a complex hierarchy of categories.
With the new A2K we get the best of both worlds. We have the preset tags from the Old A2K over in the box to the left, and we have our own customized tags we viewers and users have applied to the topics so we can find them using our own tags. For instance, instead of Yankees or baseball, you might tag it with your own labels of New York or bets, or Allstars.
To find topics using your own customized tags, click on the My Tags button at the top of the page.
When you create a new thread to start a new discussion or ask a new question you'll have the option of assigning your own tags to the topic.