Someone's "sense of humor" is their style of joking, and also the way that they react to other people's jokes. You can say that someone:

• has a good sense of humor (They don't mind people joking, and maybe they do funny things themselves.)
• doesn't have a sense of humor (They don't laugh at people's jokes. They're too serious.)
• has a witty sense of humor (They come up with intelligent jokes quickly.)
• has a sick sense of humor (They think that disgusting or harmful things are funny.)