Believe it or not, there's actually a website that describes them. Basically, wet nuts are chopped nuts in a sugary syrup. They're most populare in the New York/New Jersey area. You can purchase them from Smuckers online if you can't find them locally.
Interesting that it's only common in a small region. It would be interesting to try them, although the name could use some improving. Wet nuts just doesn't sound very appetizing.
The cartoon is just for fun. It's not often I can identify with Broom Hilda. :)