Brains (=smarts) are one of the three currencies (smarts, seduction, submission) with which you buy new cards from the selection presented to you in the top row. If you have ever played a game like Dominion, it's a very similar concept, a classical deck building game.The only cards I seem to have are TF (small amount) and the ones with the brain on them. I don't see any defensive ones.
You play your cards, accrue currency to buy new, better cards, at the end of your turn both the cards you played and the ones you just bought go to your discard pile which will eventually form your new draw pile. That's your basic gameplay loop. The cost of each card is printed in the top left corner, and the total amount of currencies is shown between both rows of cards.
Depending on your TF level the cards offered will change, in general with increasing TF you will mostly be offered smarts, then seduction, and finally submission cards. You can hover over a card in the buy row to see the TF in which it is available (note to developer: even better if this information would also be available on the cards already in your deck).
Edit: Ninja'd by dev ... ;-)