Ataranta comes from the verb atarantar, which means to fluster, stun, or bewilder someone. It's a less common, more expressive word than simply saying someone is nervous or surprised.
In the song, Luis Coronel uses it to describe how the girl's presence affects him: "Me suda la piel y me ataranta" (My skin sweats and she stuns me). It vividly conveys the intense, almost overwhelming effect her beauty has on him, making him feel completely disoriented and captivated.
Luis Coronel spends "Cuando La Miro" nursing a crush he's too shy to say out loud. It opens with "Cuando la miro, me ha robado el alma un gran suspiro" ("When I look at her, a great sigh has stolen my soul") and stays there — every verse adds another private, almost childish proof of how far gone he is: her name written "En todas mis libretas" ("In all my notebooks"), "Te amo" scrawled "En todas mis paredes" ("on all my walls"). The chorus keeps circling the same stuck question, "Cómo le hago para que sepa" ("How do I do it so she knows"), because none of that devotion has made it past the page — he still can't get the words out face to face.
It's a small, specific kind of love song: less a declaration than a rehearsal, banda horns carrying the nerve he hasn't found yet.