Hemoglobin demonstrates one of my favorite phenomenons in biology, cooperativity.
The binding curve, or the affinity of oxygen to a single hemoglobin subunit is mostly linear - meaning that if the amount of oxygen bound to hemoglobin changes only linearly with the amount of oxygen present. This is not useful - the amount of oxygen in the lungs is not dramatically different than in the brain (and other parts of the body), but you want the hemoglobin to bind oxygen in the lung, and release it in the brain.
Hence cooperativity - hemoglobin is a tetramer, being made of 4 subunits. The affinity of each subunit to oxygen is affected by the other subunits. This results in a change in the binding curve. Through evolution, the now cooperative binding curve is such that hemoglobin binds oxygen strongly at oxygen concentrations found in the lung, while it releases oxygen well at only slightly lower oxygen concentrations.
Basically, the cooperativity changes the linear (or at least low-order) phenomena found in most chemical systems to a high-order, almost binary phenomena found in many biological systems.