When you go to a place like this and they ask, what number you want your hair cut, what does this mean? (The more details you can give on this the better)

When a stylist asks “what number “ they are referring to the length you would like to see. Each number guard provides a different length . 0-being shortest and 8-being longest. Hope this helps!

Ive only heard of this for dog grooming, not people!

It could refer to the clipper guard size. If you have short hair when they use the clippers they have guards that come in different sizes or numbers that produce different lengths. Other than that I wouldn't be sure what this would reference