In terms of Classical idea:
Oxidation: Addition of oxygen or any other electronegative element to a substance .Conversely , Removal of Hydrogen or any other electropositive element from a substance.
Mg (s) + S (s) ➡MgS (s)
Similarly, Reduction is just opposite process of oxidation.
2FeCl3(aq) + H2(g)➡2FeCl2(aq) + 2HCl (aq)
In terms of Electron transfer reaction:
Oxidation: Loss of electron
Reduction: Gain of electron
Oxidant: Acceptor of electron
Reductant: Donor of electron