When a cat runs his foreleg along the side of his face, it's part of a grooming exercise. Right before he does so, he licks this "arm" until it's wet. Then he rubs it on his face like a cleaning cloth. He does this repetitively, and many times a day. While cleanliness is generally the biggest motivator, he may also do so for psychological reasons.
Your cat may be rubbing his face with his arm because he's trying to cool off. Cats don't sweat the way humans do, and getting their skin wet facilitates cooling down. Water wicks heat away from the body -- the same thing happens with humans, which is why you may feel colder stepping out of the shower than you did stepping in. Rubbing saliva on his face makes it easier to eliminate body heat.
Old Habits Return
Cats learn the importance of thorough grooming from an early age, when their mothers continually groom them with their rough, wet tongues. From the moment a kitten is born until he's about 4 weeks old, he relies on his mother to groom him with her tongue, keeping him clean and comforted. Around that age, he picks up the habit, grooming himself frequently. In fact, by the time he's an adult, he may spend half of his waking hours grooming, including wiping down his face with his arm.
He Feels Stressed
Grooming comes with a psychological benefit to your cat, so he may rub his face with his arm as a way of calming down. Stressful situations like moving, meeting a new pet or spending too much time alone may motivate your cat to revert to the methodical practice of self-grooming, which gives him a release and a sense of calm. He'll clean his face along with the rest of his body. Left unchecked, it can be harmful. Overgrooming may result in skin irritation or hair loss -- if your cat appears to suffer from these symptoms, take him to a veterinarian.
Playing It Safe
Your cat's cleaning his face with saliva is more sophisticated than the average spit-wash. His saliva is antibacterial; it can kill parasites that otherwise linger in his fur and on his skin. The process has lasting benefits, as well. Rubbing his face with his moistened arm causes a reaction in the skin glands near the roots of his hair. This causes them to secrete natural waterproofing oils that spread throughout his fur.