In Milnor Stasheff's Characteristic Classes, the geometric interpretation of Lemma 11.8 on P125 is that the diagonal cohomology class is "concentrated along the diagonal". The lemma states that
For any cohomology class $a \in H^*(M)$, the product $(a \times 1) \cup u''$ is equal to $(1 \times a) \cup u''$, in $H^*(M \times M)$.
Here, $u''$ is the "diagonal cohomology class", defined as in https://mathoverflow.net/a/74199/42662, or alternatively the image of the fundamental class of $H^n(M \times M, M \times M - \Delta(M)) \to H^n(M \times M)$.
How does the formal statement in the lemma give rise to the geometric "concentration" interpretation?