The word redox stands for reduction/oxidation. So a redox reaction is where one chemical gets reduced and another chemical gets oxidized. Reduction means that the chemical gains extra electrons and oxidation means that the chemical loses electrons. So the oxidized species basically loses electrons and gives them to the reduced species. One example of a redox reaction is the rusting of iron via oxygen.
4Fe + 3O2 --> 2Fe2O3
Oxygen (O2) is easily reduced since it is very electronegative and can readily accept electrons. So the iron goes from neutral to the 3+ oxidation state (it loses electrons so it is oxidized) while the oxygen goes from neutral to the 2- oxidation state (it gains electrons so it is reduced). In the above balanced equation, there are a total of 6 electrons involved. The electrons are transferred from the iron to the oxygen.