The power of tags (which is, behind Mavericks' new compressed memory feature, the best feature of 10.9) is in being able to pull up file searches for complex concepts, without requiring complex file naming schemes. For instance, say I'm working in Logic Pro on a new song. I remember that I did a really great guitar riff a while back, but never used it and have no idea where it is on my drives. Fortunately I had tagged the recording with the tags 'guitar' and 'riff', and so searching with those tags brings it up immediately.
Keep in mind it's also something that developers can incorporate into their apps, so for instance you might be able to configure writing software Scrivener to tag all files created with a certain template as 'novel' or 'screenplay', or tax software might tag all your forms with 'taxes' and '2013'. I really hope that the next version of iTunes starts supporting tags for music, so I can quickly make playlists by specifying tags like 'moody', 'quiet', 'female'.
I think for customers using their Macs for basic iLife kinda stuff, tagging will be helpful, but I think professional uses is where tagging will really be invaluable, especially in asset-heavy industries like video editing, 3D rendering, and music recording.