What causes clots in patients with atrial fibrillation?

Standstill. The extremely rapid rates of atrial fibrillation are in fact so fast that they create two problems: the top chamber is not mechanically moving very far at all, so it cannot shake clots loose, and the overactive atrial tissue secretes chemicals which increase the likelihood of clot formation. These processes come together to substantially increase stroke risk.
AF clots. The rapid rhythm in the upper chamber (atrium) cause a stagnation of blood flow through it - it beats too fast to force the blood through it efficiently. Because of this, the left atrial appendage (laa) is the area where >90% of the clots form in af. Clots in the laa break off and flow out of the heart and can cause a stroke. Anticoagulation - blood thing medications - reduce this risk.