First time I heard a bit more about this is in the Radio 4 interview with Tim Bernard Lee. Couldn't get my head round it. But then Tom from Stop Climate Chaos explained how it all works (it did take him 30 mins + an email to get there).
And now - I am completely hooked.
This is how I understand it - semantic web adds another dimension to information that is on the web - it links up with applications you have on your computer as well as with any other type of relevant content (photos, audio, video, maps, etc..) which is available of the web. So for example at the moment when you right-click on a link, you can 'Save a link As' or a 'Photo As' or 'copy link', 'copy link location'. What semantic web enables you to do on a right-click is to find youtube video with same tags, if the link you are clicking on is a contact - it will add it to your calendar.
The best way to understand it is to install the Operator add-on for Firefox. In IE8 and allegedly soon within Firefox there will be native support, i.e. even if the user doesn't know what they're doing, the browser will present them with options based on having read the microformats in a page.
Once the Add-on is installed, you need to go to pages that are coded using these microformats (at the moment most of the website does not have them, but in few years time this will be the standard).
Pages to look at:
or contacts, tagspaces and bookmarks:
or the geo location: