Agüité comes from the Mexican slang verb agüitarse, which means "to get sad, bummed out, or discouraged". It's a very colloquial and authentic way to express feeling down, as if your spirits have been 'watered down' (related to agua).
In the song, the singer admits, "Si me agüité, fue porque al chile me importabas" (If I got bummed out, it was because I honestly cared about you). This moment of vulnerability, using such a casual term, makes the eventual triumphant chorus of "Qué bueno que te fuiste" (It's good that you left) feel even more powerful.
Nothing beats the petty satisfaction of finally getting over someone who did you dirty, and that is exactly the vibe Grupo Frontera delivers in "Que Bueno Que Te Fuiste" (It's a Good Thing You Left). The singer airs out an ex who cheated to his face while bragging to friends that she still wrapped him around her finger. Instead of crying forever, he is taking stock of his progress: he deleted the photos from the couch, stopped dancing when her favorite track plays, and realized life is just better without her. He admits he was a bit of a fool at first, singing "Yo como siempre aquí de güey comprándote bolsas caras" (Me, as always, acting like an idiot buying you expensive bags) while she was off with another guy.
The song leans hard into authentic Mexican slang to call out the betrayal. When he says "al chile me importabas" (honestly you mattered to me), he uses the spicy Mexican idiom al chile to mean "truthfully" or "for real." He admits he got down ("me agüité", Mexican slang for feeling sad or bummed out) because she was "viéndome la cara" (making a fool out of me, literally 'looking at my face'). He does not pretend to take the high road either; he admits "sí te guardo rencor" (I do hold a grudge against you). He even tells her to keep everything he bought her, as long as she stays away. It is blunt, funny, and deeply satisfying for anyone who has ever reached the sweet relief of saying "qué bueno que te fuiste" (good riddance).