If you hover the mouse over it the map changes to various numbers and colors.
Going from guessing and a small bit of research, I believe that the numbers that show up are your final multiplier at the end of the level, and you get certain white bars around the multiplier based on how high that multiplier was. And the red squares I’m fairly certain mean that there is a challenge amulet available for that field (although, does this go away once you obtain the challenge amulet?).
Can anyone verify this?