My uncle worked in emergency wards dealing with people who came in with terrible injuries. He talked about the sketch shows they would put on to lighten the atmosphere. You often find this sense of grim humor in hospitals. The injuries people are suffering are ghastly. You have to laugh at something or you'd otherwise cry.

This quote means that when people go to the hospital with severe injuries, the atmosphere can be very depressing. To lighten their spirits, hospital staff members put on funny shows (i.e. sketch shows). This type of “grim humor” is a way to cope with the serious situations. While the injuries the patients have are horrible, laughter helps people not to feel so sad and overwhelmed. This is why they laugh at something, rather than cry.