Initially it was thought that the oxidation & reduction are just related to addition of oxygen molecule and removal of hydrogen atoms. As the process developed study showed that, its mostly related to transfer of electrons from one species to another resulting in more stable ions.

Thus in a redox reaction if one species loses electrons its considered to be undergoing oxidation reaction and acts as oxidizing agent or oxidant, and for species who accepts electrons is said to undergo reduction and behave as reductant.

This transfer is mainly based on the relative electronegativity of difference between the two interacting species. The more electronegative element attracts electrons and the electropositive element loses electrons.

For example, consider a redox reaction between Zn and HCl

Here the zinc loses electrons to a more electronegative atom Cl with the reaction for oxidation and reduction as follows:

Oxidation:

Reduction:

Thus transfer of electrons causes the redox reaction to occur.