Enviciado translates to "addicted" or "hooked". It comes from the word vicio, meaning "vice" or "addiction", so it's a powerful and passionate way to express being completely captivated by someone.
In the song, the singer says, "Tienes algo que me trae enviciado" (You have something that has me hooked). He uses this word to describe a love that is so all-consuming it feels like an irresistible addiction.
If you want to know what total infatuation sounds like in Regional Mexican music, put on "Gracias A Ti" by Eslabon Armado. The narrator is head-over-heels, opening right away by saying his crush has him hooked: "Tienes algo que me trae enviciado" ("You have something that keeps me hooked/addicted"). The word enviciado comes from vicio (vice or bad habit), but here it means he simply cannot get enough of her face and sweet lips. He claims that whenever she is around, his sadness vanishes ("Cuando ríes se me quita lo triste" ["When you laugh, my sadness goes away"]) and that time literally flies by: "Corren mis días si a mi lado estás" ("My days run fast if you are by my side").
At its heart, this is a giant thank-you note disguised as a love ballad. The singer admits that he used to feel completely alone until she became a part of him ("Ya no me siento solo como antes" ["I don't feel alone like before"]), repeating the phrase "Gracias a ti" ("Thanks to you"). He vows to protect her forever and write old-school letters detailing his feelings ("Escribirte cartas" ["Writing you letters"]). Plus, he gets cozy with the physical details, singing that her touch keeps him warm: "Tus manos me quitan todo el frío" ("Your hands take away all my cold"). It is sweet, dramatic, and completely devoted.