A grandmother is going to a store and making a list of what to buy. She's discussing the list with her friend.
Candy. I'll buy messy candy. That's what my grandchildren would like. Messy candy. If you'd had grandchildren, Mellie, they'd have been children who never ate between meals, who were sickly.
Now, basically, dictionaries indicate that "messy" is somethning dirty or causing a mess. But the last sentense makes me think that "messy" could mean some sort of food which makes children not "sickly", but roly-poly or something.