Your watchlist is a display for tracking changes, similar to the 'Recent Changes' display, but limited to showing changes only across your set of 'watched' pages. You can see the watchlist display by clicking "my watchlist" link in the top right, however this is only available to users who have registered and logged in.
Before you see anything interesting here, you must add some pages to your watchlist. Do this by navigating to a page which interests you, and clicking the 'watch' tab.
The watchlist feature is mainly useful on a very busy wiki where the 'recent changes' display becomes too "high traffic". On a typical low traffic wiki, you can normally see all of the editing activity across the whole wiki without feeling overwhelmed. On a more busy wiki you will find that many edits are taking place on pages which you personally find less interesting. To help track changes which are more interesting, start watching pages!
Typically you would watch pages related to your interest areas, and also pages where your care most about the content. If you make a significant edit to a page, you might chose to watch the page, to see if there are any follow-up edits for example. Note that there is a 'watch this page' tickbox provided on the editing screen for this purpose.
On the watchlist display, some page name appear in bold. This indicates whether or not you have visited the page to see the change. It's a bit like read/unread emails in an email inbox. The 'Recent Changes' display will also have some new bold highlighting, but for a different reason. Here bold is just indicating edits to pages on your watchlist.
See also Help:Tracking changes