What is collusion in adultery?

Collusion is a secret agreement between two or more parties for a fraudulent or illegal purpose.

Black’s Law Dictionary notes that frequently in divorce, collusion is "an agreement between husband and wife that one of them shall commit, or appear to have committed...acts constituting a cause of divorce."

Collusive divorce became an art form in the good old days.
Collusive divorce is where the opportunity to commit adultery and disposition to it came together in an inventive way known to many as a "hotel divorce." Two unhappy spouses colluded. One would give the other the evidence she (it was usually the she) needed to prove adultery. He would arrange to be in a "hot sheet" hotel room in a compromising way with the object of his affection (or sometimes just a stand-in). At the appropriate moment, the house detective would open the door and private detective, camera clicking, captured the two of them in the midst of their assignation.

The tail wagged the dog, in a manner of speaking, but the photographic evidence met the test and filled the bill (particularly when the parties also arranged to be in a state of undress).