Only certain villagers can catch crabs. If you watch them for awhile, you'll see them emerge from the sea carrying a crab (and celebrating their catch).

Actually I never realised but my villagers have found 1082 Crabs, I went to main menu > Puzzles and theres a button Stats

the cool part is that the crabs are worth 55 food points!

One of my villagers caught crabs. But with the help of a technologically gifted monkey, we were able to earn enough tech points to clear up the matter. However, upon now learning that the crabs are worth 55 food points, I will be breeding my infected villagers to better 'spread the wealth', if you will.

what a nice monkey.