"Ich mag es, Obst zu essen." and "Ich esse gern Obst." both mean the same, but they are used in different constructions. Mögen is a verb. It's often used in Präsens: "Ich mag Tiere." (I like animals.) or in Konjunktiv: "Ich möchte ein Eis." (I want ice-cream.) In colloquial German you might also hear: "Ich mag jetzt in den Zoo." (I wanna go to the zoo.)

Gern on the other hand is an adverb, so it's only used together with a verb, meaning the verb is done with joy "Ich spiele gern Gitarre." (I like playing the guitar.) or willingly "Das mache ich doch gern." (="I'll gladly do that." -> Don't mention it.) In connection with haben it means love or like: "Sie hat ihr Haustier gern." (She likes her pet.)