The ‘mod’ in the expression above comes from modular (or clock) arithmetic. It’s a system in maths where the numbers jump back to zero after a certain integer. Clocks work mod 12 as the moment you reach 12, you’re actually back to 0.
For a bit more clarity, examples might be nice:
4 ≡ 1 (mod 3);
7 ≡ 1 (mod 3);
14 ≡ 2 (mod 12) and so on.
Anyhow, the story behind this wacky graph is that my friend was looking to practice his graph sketching skills and this function somehow popped into my mind.
Lo behold, I plugged it into Wolfram Alpha and got an awesome graph. The moral of the story? Play with Wolfram Alpha!