"אנחנו אוכלים את הגבינות."
Translation:We are eating the cheeses.
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Without it, the sentence would be grammatically incorrect. את is used to introduce the definite direct object, which here is הגבינות. Without it, the object would be indefinite. Here's another example:
אנחנו אוכלים תפוחים = we are eating apples
אנחנו אוכלים את התפוחים = we are eating the apples
Yes, ה is the definite article, but את is also required when you have a direct object. Your example is grammatically incorrect, because you can't omit את in such a sentence. When there is a direct object which is definite, Hebrew requires both את and ה.
הם אוכלים את התפוזים - they are eating the oranges
אני שותה את המיץ - I am drinking the juice
אתם רואים את הילדים - You see the children
Since the object is definite, leaving out את would be a mistake.