Since redox reactions concern the loss (oxidation) and gain (reduction) of electrons, the elements involved exhibit either electronegativity or electropositivity. Electronegativity measures an element's ability to gain electrons and electropositivity measures an element's ability to lose electrons.
In the equation:
Cu2+ + Mg ® Cu + Mg2+
Mg loses electrons (exhibiting electropositivity) and Cu gains electrons (exhibiting electronegativity).
The wording can get tricky. Cu is the oxidant (oxidizer) oxidizes the other element. Cu gains electrons. Mg is the reducer. Mg reduces Cu (gives it 2 e-) and so Mg loses 2e-, becoming Mg2+.
This site helps: http://www.chemguide.co.uk/inorganic/redox/equations.html#top