Here’s an example:
A user visits my Comic Collector product page. Maybe he clicked my search ad on Google, or an image ad on the Content Network, or the Comic Collector listing in the organic results. It doesn’t matter really, he may even have come from Bing, or a link on a comic forum discussing cataloging software. This user doesn’t buy and leaves the site (annoyingly, that still happens to us sometimes Maybe he downloaded the trial edition, maybe not.
Now after he visits my website, this user goes on to browse the internet, visiting other websites. And suddenly everywhere he goes, he sees Comic Collector ads. Site-wide leaderboards, towers, inline rectangles, even little text ads. My ads are following him around, almost stalking him.

One important thing to understand: remarketing ads do not only appear on websites related to your product, like your “normal” content network ads. No, they appear everywhere, on any site.
Remarketing let’s you target specific users wherever they go, as opposed to all users on specific websites.