Russian verbs don't explicitly have the "-ing" form, so there is some ambiguity when going between English and Russian (for example, "я живу там" can mean either "I live there" or "I am living there"). The difference between ест and ем is one of conjugation (see JanisaChatte's response above, which gives all the conjugations for the verb). Both can translate to either "eating" or "eat" depending on context.
Why is где он ест translated as "where does he eat" rather than "where is he eating"? The latter seems more correct to me. The former implies that he eats somewhere regularly (but that he may not be there at this moment) and the speaker wants to know where that is. The latter implies that he is somewhere, right now, eating. Isn't that what the Russian sentence means?