You mean the scope images? Those are to check the performance (brilliance) of the diamond.
For certificate, stick to GIA or AGS. They are the better ones. Personally, I prefer AGS over GIA, but that's just my preference.
Most people will recommend you to go for a minimum 3 EXC (GIA) diamond.
Cut - Excellent
Polish - Excellent
Symmetry - Excellent
It's a good start.. but there is still much more to it. There are many 3 EXC out there that are still badly cut even though it shows "Excellent" on the cert. Don't just follow the 3 EXC blindly. To make sure you're getting a good 3 EXC, you can follow these steps.
1. Make sure the proportions are good.
How - Use the HCA tool
Holloway Cut Advisor | HCA Tool | PriceScope
Aim for a score between 0.4 - 1.5
2. Make sure it has good light performance
How - Use the Ideal and Aset scope to check. This is the colorful scope images you saw.
3. Make sure it has nice hearts and arrows
How - Use the hearts and arrows scope.