Emborrachar literally means "to get drunk". It's a common verb, but the way it's used in this song is purely poetic and very memorable.
Luck Ra sings, "Quiero emborrachar mi corazón" (I want to get my heart drunk). He's not talking about literally giving his heart alcohol; he's using this powerful metaphor to express his desire to be completely overwhelmed and intoxicated by the feeling of love. It's a creative way to describe wanting to fall deeply and completely for someone.
Picture this: it is thirty degrees out ("Treinta grados"), the sun is melting everything, and the speaker's friends have already started on the drinks. Most summer anthems stop right there, but Argentine cuarteto singer Luck Ra turns the script upside down. He admits that being single is fun, but he is completely fed up with the alcohol ("Ya me cansé de la bebida") and wants something real. What he wants is a summer fling that actually sticks around: "Ando buscando un amor... De verano, pero, duradero" [I'm looking for a love... of summer, but lasting]. He flips the classic beach party routine into an honest search for romance.
The imagery stays hilariously literal and sun-baked. Instead of beer, he insists that his thirst is for kisses at sunset on the sand ("Tengo sed / Pero de unos besitos al atardecer" [I'm thirsty / But for little kisses at sunset]). There is also a great conversational Spanish idiom to learn here: "Si alguien está en la misma / Díganle, escucho ofertas" [If anyone is in the same boat / Tell them, I'm taking offers]. In everyday speech, "estar en la misma" means you are dealing with the exact same mood or situation as someone else. He jokingly leaves the door wide open for any applicants ready to sit around doing nothing together until dawn.