It means humor that is unsophisticated, or jokes that are so old that everybody already knows them. Corny joke are often bad pun, particularly one that everyone has heard before. "Why are there fences around cemeteries?" "Because people are dying to get in!" ("Dying to" is an idiom for "wanting to.") Joker: Knock, knock. Victim: Who's there? Joker: Mary. Victim: Mary who? Joker: Mary Christmas! [Merry Christmas]

"Corny" humor is like this: https://www.youtube.com/watch?v=bXysRO11Xi8 GLOOM, DESPAIR AND AGONY ON ME From the TV Show "Hee-Haw" (1969 -1992) Buck Owens & Roy Clark Gloom, despair, and agony on me Deep, dark depression, excessive misery If it weren't for bad luck, I'd have no luck at all Gloom, despair, and agony on me We figured she was rich, loaded to the hilt And we figured she had class like the Vanderbilts 'Cause we had heard for years how she was so well reared How was we to know they meant the way she was built Gloom, despair, and agony on me Deep, dark depression, excessive misery If it weren't for bad luck, I'd have no luck at all Gloom, despair, and agony on me

Foster Brooks as the Drunk Airline Pilot in a bar with Dean Martin https://www.youtube.com/watch?v=6jNNFqQODKE

"What does 'a corny sense of humour' mean?" A sense of humour, of this type: http://www.thefreedictionary.com/corny I think "Dad jokes" are typically corny.

Jonathon Winters improvising a flight on an Airplane, sitting next to a celebrity, Dean Martin https://www.youtube.com/watch?v=1hcgXXJk_nw .