Poppy straw is a term for the stems and pods of various species of poppy. It is harvested to extract various opiate alkaloids from, which are then refined and synthesized for various pharmaceutical purposes.
The traditional way to harvest opium is from the ripe seed pods of the opium poppy, Papaverum Somniferum. The latex of the seed pods is the most rich source of alkaloids, especially morphine. However, its harvesting is very labor intensive, and since it is labor intensive, it is also prone to illicit diversion of the product. Poppy straw has a very low concentration of active components, such that to divert it to illicit purposes would be prohibitively difficult: it would probably take a pickup truck full of stems to make anything usable. In addition, much poppy straw is made from species of poppy (such as the Oriental Poppy and the Iranian Poppy), that produce much more thebaine than morphine. Thebaine is (to most people) not a recreational drug but can be used as a precursor to other drugs.
Thus, the usage of poppy straw is a way to mechanize the harvesting of poppies and to decrease the chances that opiates can be diverted. While the old method is still in usage in the third world and in places where the growing of poppies is mostly illicit, the poppy straw method is the method used in the first world, and where much of the world's supply of pharmaceutical opiates comes from.