Pick a bottom number. We find the best fraction for π with it, then score how close it got.
Most fractions score about 1. A rare few spike above 2 — 355/113 scores about 3.2. Notice the spikes shrink toward 2 as the bottom number grows. The new paper claims that's no accident: past some point, no fraction can stay above 2 by any fixed margin. That's what “π's irrationality exponent is 2” means.