“Donner sa langue au chat” is a french idiom that literally means “to give one’s tongue to the cat” and it means
you can't find the answer to a question or a riddle so you ask for the answer.
For this video, this idiom is used to create a link between language and tongue which are the same word in french : “langue”. The point is to introduce linguistics in a simple way. This particular video explains what a pleonasm is.