As with most new things, it takes a few different exposures to something before I decide to take a look at it. I heard about bloglines several times before I started using it, and the same is true with Delicious. Now I use both of them on a daily basis.
In short, it’s a way to have your bookmarks accessible from anywhere, in any browser. It also allows you to see what other people are bookmarking. I had been keeping a collection of links (I had more than 200 entries) so I used Cameron’s migration script (tweaking it fairly heavily and spending a half hour getting all of the required Perl CPAN modules) to upload all of my links.
Now when I run across a site I want to bookmark, I just click the del.icio.us bookmarklet and up pops a window with the link and title in it. I then modify the title to my liking, add a few tags, and save it. It’s very efficient and later on I can easily retrieve those links by tag, chronologically, or by searching for it.
If you’re interested in trying it out for yourself, you might find John’s explanation us.ef.ul.