A raccoon's forepaws carry a very high density of mechanoreceptors, and a disproportionate share of its somatosensory cortex is devoted to processing signals from them. Wetting the paws makes the covering layer more pliable and improves tactile sensitivity, so handling an item underwater or in wet hands yields more information about it than handling it dry.
The behaviour appears in captivity far more than in the wild, where raccoons often do a version of it while foraging in shallow water for crayfish, frogs and molluscs, feeling under stones for prey they cannot see. Captive animals with no need to search perform the motions on dry food beside a water dish, which is consistent with a fixed foraging pattern being expressed without its usual context. Raccoons do not reject dirty food and will eat it unwashed.
Raccoons are also genuinely good at mechanical problems. Early twentieth-century experiments found them opening complex latches, and modern work shows them solving multi-step puzzle boxes and remembering solutions for long periods. How much reflects general problem-solving rather than exceptional dexterity has not been separated, and the two are hard to test apart.