Web clips were originally a subtle, background kind of RSS reader for your Gmail inbox. These days, they're mostly advertising. Not that Gmail shouldn't make money, but if you'd like to see one less ad, turn Web Clips off in your settings.
If you're logged into Gmail/Google right now, head to the Web Clips page in Settings and disable them with one checkbox click. Technically, you can see the RSS feeds, news sources and other headlines you selected in the Web Clips section if you click the left/right arrows to the right in the Web Clips toolbar, but most people don't want to manually move past ads.
Big thanks to Google Operating System, the blog that noticed the recent ads-first-then-news transformation of Web Clips.
Gmail's Web Clips, Now With More Ads [Google Operating System]