There are two verbs in Russian that are homonymous in one of their forms: these are есть meaning "to eat" (infinitive) and есть meaning "(it) is" (third person singular present from быть "to be").
These verbs are not cognates (itthat means that they're not connected etymologically), they just happen to be homonyms in that one form and only in Russian, and not even in its most closely related languages, Belorussian and Ukrainian. Before the spelling reform of 1918, they weren't even homographs; they were spelled есть "(it) is" and ѣсть "to eat", using historically different root vowels.
The Russian language exhibits a phenomenon called "proximal possession". A common way to express the 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, to address your question, the word ест does not mean anything other than "(he) eats". However, its infinitive form, есть "to eat", does indeed have a homonym with the meaning "have", although 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 vegetables in his fridge.