Instances are finite sets of pixels. The intersection over union of two such sets is the size of their intersection over the size of their union (with the convention that the IoU of two empty sets is $0$). A prediction is matched to an annotation when their IoU exceeds a threshold, and the published metric uses the threshold $½$ with a strict inequality.

The first statement is why this threshold makes the matching unambiguous on the annotation side: distinct annotations of one image are disjoint, and no prediction can exceed IoU $½$ with two disjoint sets. The second statement shows that the strictness is necessary: with $≥ ½$ a prediction can tie the threshold with two disjoint annotations. The third states both at once: $½$ is the infimum of the thresholds under which a prediction matches at most one annotation.