Currently, when you search for, say, "Target," search results include the big box retailer's website, Google Maps results for nearby locations, and various links to the company's apps, social media accounts and Wikipedia entry. If you enable Gmail integration with your search results, emails you've received from Target -- such as order receipts and coupons -- would also appear in the right-hand column. Google's also promising to include your upcoming flights into results for airline information, based off of your email confirmations.
This is just another step in the direction of Google's vaunted "Universal Search" initiative. Earlier this year, the company introduced Search Plus Your World, which adds Google+ information to search results. Perhaps the best example of the Universal Search ideology is the Google Now functionality built into Android 4.1, a.k.a. Jelly Bean.
If you want to add your Gmail results to Google, head over to the appropriately named "Gmail in personal search results" page and sign up for the trial. AllThingsD reports that activation could take a few days, but the buzz we've heard about it on social media indicates that most people are being enrolled in a matter of minutes.