Rencor translates to "grudge" or "resentment". It's a powerful word that describes the feeling of bitterness you hold onto after someone has wronged you.
In the song, the title itself is "No Te Guardo Rencor", which means "I don't hold a grudge against you." The singer uses this phrase to tell his ex that even though he's heartbroken, he wishes her the best and is letting go of any negative feelings, which is a very mature and compelling sentiment.
This song is the perfect example of someone trying really hard to act like they're over a breakup, but failing completely. Fabiø Guerra starts off by saying he heard his ex is happy, and then immediately claims, "No es por presumir mi amor pero me va mejor a mi, sin ti" (Not to brag my love, but I'm doing better without you). It's a classic move, but the whole story comes crashing down right after.
He admits he doesn't know how to get her out of his head and, in a very relatable line, says he has no idea how to tell his mom "que por amor su hijo es un desastre" (that because of love, her son is a disaster). He's so obviously heartbroken that the bartender won't even charge him for drinks. Even though he repeats the title line "no te guardo rencor" (I don't hold a grudge against you), his actions tell a different story. He's wandering the streets, getting drunk, and feeling completely lost. It's a song about trying to be the bigger person while your heart is still in pieces.