Characteristics of myoglobin 
Myoglobin is a relatively small protein of mass 17.8kDa made up of 153 amino acids in a single polypeptide chain. It was the first protein to have its three-dimensional structure determined by x-ray crystallography by John Kendrew in 1957. Myoglobin is a typical globular protein in that it is a highly folded compact structure with most of the hydrophobic amino acid residues buried in the interior and many of the polar residues on the surface. X-ray crystallography revealed that the single polypeptide chain of myoglobin consist entirely of alpha-helical secondary structure. In fact there are eight alpha-helical secondary structure in myoglobin. Within a hydrophobic cervice formed by the folding of the polypeptide chain is the heme prosthetic group. This nonpolypeptide unit is noncovalently bound to myoglobin and is essential for the biological activity of the protein. Myoglobin is a small oxygen-binding protein found in muscle cells. Its functions primarily in storing oxygen and facilitating oxygen diffusion in muscle tissue. Myoglobin is a single-chain globular protein that consists of 153 amino acids and a heme group (an iron-containing porphyrin). The globular structure of myoglobin consists mainly of alpha helices linked together by various turns. Myoglobin exists either in an oxygen free-form called deoxymyoglobin or in a oxygen bound form called oxymyoglobin. Whether myoglobin binds to oxygen depends on the presence of the prosthetic group, heme. When myoglobin is able to bind to oxygen, it serves as the primary oxygen-carrying molecule in muscle tissue. Normally, the iron group in myoglobin has an oxidation state of 2+. However, when oxygen binds to the iron, it gets oxidized to an oxidation state of 3+. This allows the oxygen that is binded to have a negative charge, which stabilizes it. Myoglobin's affinity for oxygen is higher than hemoglobin. And unlike hemoglobin which is found in the red blood cells, myoglobin is found in muscle tissues.
Myoglobin owes its high affinity for oxygen to several factors. First, it has a proximal histidine group that helps it bind oxygen. Once the oxygen has been successfully bound, the structure of myoglobin comes into play. It prevents the reactive oxygen species from escaping by modifying the intrinsic reactivity of the heme group. Specifically, the ferrous ion coordinated with the dioxygen in the heme group can be oxidized to a ferric ion coordinated to superoxide. By keeping the reactivity of the oxygen under control with help from its structure, therefore, myoglobin can bind and hold on to oxygen atoms.
Although it has a much higher affinity for oxygen than its structural analog hemoglobin, myoglobin is a less efficient oxygen carrier for the cell. Because its affinity for oxygen is so high, myoglobin has a difficult time "letting go" of oxygen in the right areas. The cell needs oxygen to be distributed to the appropriate organelles, just as the body needs oxygen to be distributed to the right organ systems. This means that the species that "carries" the oxygen must be capable of releasing it once it reaches its assigned destination. Myoglobin's high affinity for oxygen means that it will be less inclined to release the oxygen once it has been bound; this in turn means that myoglobin will be distributing less oxygen to those areas where it is needed. Thus, hemoglobin is actually a more efficient oxygen carrier for the cell since its affinity for oxygen is lower. A lower affinity means that hemoglobin will have a significantly easier time releasing oxygen in the correct areas of the body. For this reason, the cell relies more upon hemoglobin to distribute oxygen than it does myoglobin; however there are specific areas of the body for which myoglobin is the better oxygen-carrier, such as for muscle cells. More can be read about hemoglobin in the hemoglobin section.
Another consequence of myoglobin's high affinity for oxygen is a higher affinity constant (KD). Since the affinity constant represents the concentration of substrate at which fifty percent of a protein's active sites are saturated, this means that half of myoglobin's active sites will be saturated with oxygen at a much lower concentration than for hemoglobin. More can be read about the affinity constant in its appropriate section.
Haemoglobin, the analog of myoglobin, consists of four poly peptide chains, two identical alpha chains and two identical beta chains. Each of the subunits contains a set of alpha helices in the same arrangement as the alpha helices in myoglobin. This structure that recurs is called a globin fold.
The oxygen-binding properties of proteins can be observed by viewing its oxygen-binding curve. An oxygen binding curve is a “plot of fractional saturation versus the concentration of oxygen”.
Real world examples: How is Myoglobin used? 
Myoglobin is actually used in conjunction with troponin to assist in the diagnosis process of a heart attack. Myoglobin levels appear to rise within two to three hours of a heart attack or other muscle injury. These levels reach their peak within eight to twelve hours, but usually fall back to normal within one day. The reason myoglobin is used as the key marker is because it turns positive far sooner than troponin. A positive reading may or may not signal potential damage of the heart, so it often can be ambiguous. Thus, a positive result is assessed based on troponin testing. However, a negative myoglobin result rules out a heart attack altogether. Another interesting fact regarding myoglobin is that it is highly toxic to the kidneys and if severe muscle injury occurs, blood levels of myoglobin may rise quickly and the kidneys (which function includes: releasing myoglobin in the blood as urine) can be severely damaged due to the increase amount of myoglobin. Another cause of increased myoglobin content is strenuous exercise, in addition to heavy alcohol abuse. In regard to muscle contraction, as fibres contract, they sqeeze the walls of the capillaries thus reducing or even stopping blood flow completely. It is actually during these situations when myoglobin has the ability to release its oxygen. It seems apparent that myoglobin plays the role of a hero. As the muscle relaxes, flow is restored and myoglobin is then recharged using the oxygen supplied by its oxygen-carrier partner, hemoglobin. These actions cause muscle injury and increased myoglobin in blood, which ultimately result in kidney failure.
Myoglobin's further importance 
Myoglobin plays the pivotal role of acting as an oxygen store during times of severely reduced blood oxygen supply. This notion of course is well established. What is also interesting to note is the fact that in terrestrial mammals, myoglobin compensates for the reduced blood flow in the crucial organ of the heart in addition to skeletal muscles during contraction.
Berg, Jeremy. Biochemistry . 6th. New York : W. H. Freeman and Company, 2006.
Nelson, David. Lehninger Principles of Biochemistry. 5th. New York : W. H. Freeman and Company,2008.