Oxygen travels through the human body by being bonded to the iron in a special molecule in blood cells called hemoglobin. This is necessary because, unlike carbon dioxide, oxygen dissolves very poorly in water. Despite this, a few organisms with very slow metabolisms, such as sea stars, only use water to carry oxygen in their bodies, while others use copper instead of iron to bind oxygen in their blood.
Different gases have different solubility in water, which is the main fluid in blood. The whole purpose of red blood cells in humans and other vertebrates is to carry oxygen, which dissolves very poorly in water. The solubility of gases goes down with temperature, so the water in blood carries even less oxygen than the colder water of an ocean or lake. Since oxygen is essential for aerobic metabolism, animals with faster metabolisms require a way to get more oxygen to their cells than dissolution in water would provide.
The iron in hemoglobin provides a place for oxygen to bond to, creating a new chemical compound rather than dissolving in water. The rest of the hemoglobin molecule, consisting of four peptides, controls what binds to the iron and also helps it to be released readily.