I almost put the word may instead of will in the title, but that would have been denying an obvious and inevitable future. Google+ (G+) is ultimately about monetization, and traditional AdWords/AdSense ads aren’t going to cut it.
Remarketing on steroids
Google’s advertising intentions with G+ have been front and center since the launch of their field trial. On the sign up page there’s a check box that states:
“Google may use my information to personalise content and ads on non-Google websites.”

To what degree checking this box or not checking this box will affect advertising on non-google websites is anyone’s guess, but you can be assured that the data will be used on Google’s properties.
Similar to Facebook Ads, G+ will provide an entirely new level of demographics and user interests for advertisers. This data will be used to enhance current methods of remarketing, creating a much more targeted and personalized ad experience for the user. That includes using your name, interests, and possibly referencing people in your circles.
New ad types
Similar to Facebook Ads and other non-standard ad formats like The Deck, Google will have the opportunity to reinvent how ads look and function in G+. Expect new dimensions and template options, like the ability to include a person’s name or interest. Another possibility is sponsored posts that appear in the G+ stream. With G+, Google has the opportunity to reinvent their advertising product. Here’s a mockup of how ads and sponsored posts may appear.

Higher ad costs
If Google can greatly improve its audience targeting through the use of G+ data, then they will most certainly charge a premium for it, and advertisers will be willing to pay for it. If you want to know why G+ is so important to Google, it’s because it’s the second coming of advertising for them. And all along you thought it was mobile…silly rabbit.