se creuser la tête

to think very hard trying to work something out

Used for straining your memory or your thoughts to solve or recall something, what English calls racking your brain.

Je me creuse la tête depuis une heure pour trouver un cadeau original.

I've been racking my brain for an hour trying to think of an original gift.

Origin uncertain. The image is fairly transparent on its own: digging into your own skull the way you'd dig into the ground looking for something buried.