If studying philosophy, the term evil genius comes up when you get into the post Renaissance work of Descartes. What Descartes wanted to do was do away with all sense based knowledge, which could in fact be false, and get down to a kind of foundation upon which he could establish a kind of pure knowledge, based on things which could be rationally understood with the mind.

What he ends up starting with are simple truths of mathematics, which can be known, and proven to be true. Unless there happens to be an evil genius (sometimes translated as evil demon) with all the power of God making everything false that Descartes sincerely believes. Then we'd be in trouble, wouldn't we?

Using the "evil genius" theory, Descartes thinks he has rationally proven the existance of God, because there must be some great benevolent force out there which would prevent such an evil genius from making false all which we know to be true. Thank heavens.