I deal with Vallejo, so I will refer to it.

Vallejo has 16 primer colors. Your normal White, Grey, and Black, but also colors like German Dark Yellow, German Grey, US Olive Drab, Russian Green, UK Bronze, Green, etc, etc.

If you are building say a US Sherman tank, you can use the colored primer as your basecoat (instead of the usual grey primer and then layer of OD green paint).

With the primer and color in one, you end up putting less layers of paint on your model, and thus less paint to obscure details. One less step to do, and saves you time in your build.