Platelets, also called thrombocytes (thromb- + -cyte, blood clot cell), are a component of blood whose function (along with the coagulation factors) is to stop bleeding by clumping and clotting blood vessel injuries.
Milk of the poppy is essentially the Westeros version of morphine. Maesters make it from crushed poppy flowers, and morphine and other opiate-based drugs are made from poppy plants. Indeed, the books' descriptions strongly suggest that the poppy is intended to be the real-world opium poppy (Papaver somniferum).
Poppy seeds are also used as a flavorful ingredient in many popular foods, including muffins and bagels. Although poppy seeds used in food are produced legally, they can contain high enough levels of the opioid to trigger a positive result on some types of drug urine tests.