Essen (to eat) changes form depending on the subject: ich esse (i eat), du isst (you eat), er/sie/es isst (he/she/it eats), wir essen (we eat), ihr esst (you (plural) eat), sie essen (they eat).
If the subject is a noun instead of a personal pronoun, the third-person form is used; so, isst for a singular noun (Der Mann isst - the man eats), essen for a plural noun (Die Männer essen - the men eat).
They're pronounced the same. Normally it's pretty clear from context, but in an artificial situation like this the speaker could just as easily be saying "Der Mann ist"; you just have to remember we're mostly learning "essen" this lesson ;-)
Either is a correct translation! You can use it to mean "The man eats" or "the man is eating (now)"
In the German language verbs are conjugated like this - not just "eat" in fact. It helps to look at the conjugation tables to get used to the patterns, as well as going over these sentences to get used to it in context. Later on it will be second nature :)
English also has verb conjugations, it is just not so obvious and complicated any more. Think of "to be" that can take the form of am/is/are. Then you also add an "s" to verbs for singular, whereas you do not for plural subjects. It is all a form of conjugation in English. German (and many other languages too) just have a more elaborate conjugation system. So it takes getting a little used to.