Alivianado is a popular Mexican slang term that means feeling relaxed, unburdened, and generally doing well. It comes from the verb aliviar, which means 'to relieve' or 'to soothe'.
In 'Andamos Mejor', the singer uses alivianado to describe his new state of mind after overcoming hardship. He's no longer worried about money and can finally enjoy a more relaxed life, perfectly capturing the song's triumphant theme.
This song is a straight-up celebration of making it. Los Gemelos De Sinaloa lay out a story of going from having nothing to enjoying the good life. They start by saying, "Si antes no cargaba ni un peso en la bolsa / Ahora todo cambió" (If before I didn't even carry a peso in my pocket / Now everything changed). It's a classic success story about leaving hard times behind.
But this isn't about luck. The singer makes it clear he earned his success through hard work, a value his parents instilled in him. He says if you see him "ruleteando en un carrito bien, del año, es porque le chingué" (cruising in a nice, new car, it's because I worked my ass off). He also gives credit to a higher power for watching over him, saying he's doing better now "gracias al Señor" (thanks to the Lord). The whole track is an anthem for anyone who has worked hard to improve their situation.