The reason behind the browning of steaks, along with almost all types of foods, is called the Maillard Reaction. The Maillard Reaction causes the amino acids and simple sugars in these protein powerhouses to rearrange in such a way that they reflect brown light. What creates the Maillard Reaction is the high temperature during the cooking process. However, the high temperature needs to boil away the water in the steak in order for the amino acid and simple sugar to rearrange. The boiling away of the water, which has a low boiling point at atmospheric pressure, allows the steak to reach an even higher temperature. This is also the reason why pressure cookers work, which increase the boiling point of water, allowing for higher temperatures to be reached.
Heat transfer is what causes the steak to cook, where heat from the flame transfers energy through the pan to the steak. Specific heat also relates to this, as the pan is made of metals and has a low specific heat. The fire from the butane gas stove burns at around 1100F. The base of the pan that first comes in contact with the flame is made of copper, which has a specific heat of 0.385 J/(g* C). This means that the pan only needs 0.385 joules per gram to increase in temperature by 1 degree Celsius. Because it takes so little energy to heat the pan, this is why it can cook the steak through.