A hydrogen ion is formed when a hydrogen atom loses an electron and therefore becomes positively charged (it has a charge of +1). A hydrogen atom is therefore often referred to as just a proton, as it is left with only one proton and no electrons, as a H atom only has one of each. Hydrogen ion can also be written as H+.
pH is a measure of an atoms ability to dissociate from a hydrogen ion. The more easily it does this, and consequently the higher the concentration of hydrogen ions in a solution, the lower the pH. Substances with a pH lower than 7 are known as acidic. Consequently, hydrogen ions are important to any reaction dealing with acids and bases, and as such are extremely important to chemistry.