I see this all the time in recipes, but I have never been sure as to
what it means. Does it mean brown to the point that there is a crispy
crust, or does it just mean to cook until the pinkness is gone?

I usually try to put the crust on for solid pieces of meat, but with
hamburger I usually interpret it to mean that I cook the burger to the
point that I can chop it into small chunks using something like a wooden
spoon.

Enquiring minds want to know.