In hair salon talk...what does "double process" mean? It's a form of coloring apparently?

I'm looking up new places to go for my hair. I'm happy with my guy, but when it comes to color...well I prefer to change. He's lazy with it and it never turns out right. I will go to him for cutting because he does an amazing job with it and really knows what he is doing. It took years to find someone in my area that actually knows how to cut hair. I found a place and I found a few others for the coloring online (they have websites for their shops)...I keep seeing "double process" under the color section on all of these different websites. What does that mean and what should I be getting when I go?
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salon websites