To the average user, the only real difference is the ability to switch between the two cameras and the added "Portrait Mode" feature coming in IOS 10.1. However, if you want to get technical, the situation isn't as simple as it seems.
The iPhone 7 has one 12mp Camera with a 28mm Wide Angle F/1.8 Aperture 6 Element lens. On the other hand, the iPhone 7 Plus has two 12mp Cameras one with a 28mm Wide Angle F/1.8 Aperture 6 Element Lens (same as the non-plus) and Second one with a 56mm Telephoto F/2.8 Aperture 6 Element Lens.
However, and this is where things get tricky, the iPhone 7 Plus is actually almost always using both cameras at the same time, using something called "Computational Photography". Now to the average user, you may never actually notice a difference. However, this could lead to the iPhone 7 Plus having improved dynamic range, improved noise reduction, and improved image sharpness.