Hemoglobin is an iron-containing protein in red blood cells that transports oxygen from the lungs to tissues and carbon dioxide from tissues back to the lungs. It contains a heme group with iron that reversibly binds oxygen. There are two forms - relaxed R form when oxygenated and taut T form when deoxygenated. Factors like oxygen partial pressure, pH, carbon dioxide levels, and 2,3-bisphosphoglycerate affect hemoglobin's affinity for oxygen. The Bohr effect describes how protonation of hemoglobin in tissues increases oxygen release for cellular respiration.