The age old question... I think it is different for everyone. If I had to sum it up in a single word, I'd use "exaggeration." Gags are usually funny because they take an idea that rings true but exaggerates the circumstances. For example, everyone used to know what it was like to need to use a payphone but not have change. Gary Larson once drew a Far Side where 2 people were stranded on a small island with a payphone. One was standing by the phone expectantly looking at his co-strandee who was sitting on the beach. The one sitting said something like, "For the 100th time in as many days, I don't have a quarter!"
Characters are similar. It doesn't matter if they are people, aliens, or animals. They should have human characteristics we all identify with, just somewhat exaggerated. Hope that helps!