Originally a math term from
abstract algebra roughly meaning "if you ignore
differences depending on X." For instance, there are 8 ways to rotate or flip a square. But suppose you color one pair of opposite corners red, and the other pair green, and consider orientations of the square that look the same to be the same ("to modulo out by the relation that considers opposite corners to be the same"). Then rotating the square by 90 degrees becomes the same as
flipping it horizontally or vertically, and rotating the square by 180 degrees becomes the same as doing nothing. Then there are only 2 ways to rotate or flip the square.
Used colloquially by mathy people to mean, roughly, "if you ignore the fact that."
1) We had a great capture-the-flag game, modulo a few sprained ankles. ("If you do not consider a few sprained ankles to change whether the game was good or not, then we had a
good game.")
2) I'd love to go for a drink with you, modulo that I don't drink. ("You invited me for a drink, and I'd love to
do something of
equivalent enjoyment that does not depend on whether or not I drink.")