The elements involved in an electrochemical reaction are characterized by the number of electrons associated with each atom of the element. This number of electrons is often expressed in terms relative to the number of electrons such an atom would have when electrically neutral. The term used for such an expression is the oxidation state of the atom.
For example, oxygen has 6 positively charged protons, and thus in the neutral state would also have 6 (negatively charged) electrons. In dihydrogen monoxide (ie, water), each oxygen atom can be viewed as surrendering two electrons, one to each of two hydrogen atoms. The oxidation state of each oxygen atom in water then is -2, and of each hydrogen atom in water is +1.
In the nomeclature of chemistry, the substance losing electrons is said to be the reductant and is oxidized' by the the other substance(s) in the reaction which gain the electrons.
The substance gaining the electrons is said to be the oxidant and is said to be reduced (by the reductant).
Though historically oxidation, as the name suggests, many reactions not directly involving oxygen, but involving changes of oxidation states, (redox reactions) are possible.
This is a simple example, because oxygen and hydrogen have few oxidation states at the temperatures and pressures commonly found on Earth. However, many of the transition metal elements each have a rich variety of commonly occuring oxidation states.
A spontaneous electrochemical reaction can be used to generate an electrical current. This is the basis of all batteries or fuel cells. For example, gaseous oxygen (O2) and hydrogen (H2) can be combined in a fuel cell to form water and energy (a combination of heat and current, typically).
The reverse case, for non-spontaneous electrochemical reactions, can be driven forward by the application of a current at sufficient voltage. The electrolysis of water into gaseous oxygen and hydrogen is the appropriate example of this.