There are two verbs in Russian which are homonymous in one of their forms: it's есть meaning "to eat" (infinitive) and есть meaning "(he) is" (third person singular present from быть "to be"). These verbs are not cognates (meaning they are not connected etymologically), they just happen to be homonyms in that one form.
Russian language exhibits a phenomenon called "proximal possession": a common way to express a concept of "someone having something" is saying, literally, "at someone there is something".
У меня есть машина would mean "I have a car", or, literally, "there is a car at me".
So, answering your question, the word ест does not mean anything other than "(he) eats". However, its infinitive form, есть "to eat", has a homonym with a sense of "having" indeed, though it's not its primary meaning and it's only a homonym in one particular form.
Есть овощи полезно для здоровья // Eating vegetables is good for your health.
У него в холодильнике есть овощи // He has some veggies in his fridge.