Casi algo literally translates to "almost something". It's a popular modern term to describe a relationship that is more than a friendship but never becomes official—a romantic situationship that ends before it truly begins.
In the song, Xavi uses this phrase to define a failed romance. He refers to the person as his casi algo (almost something), casi todo (almost everything), and casi siempre (almost always) to express the bittersweet feeling of what could have been, but never was.
This song is the ultimate anthem for ending a 'situationship'! Xavi is telling someone to stop calling and messing with his life, saying, "Ya no llames al phone / Deja de estar jodiéndome la vida más" (Don't call my phone anymore / Stop messing up my life). He's so done with the games that he claims he knows all her tricks: "Túmbate el rollo, ya conozco tus mañas" (Cut the act, I already know your tricks).
The best part is how he defines what they were. He asks why they should pretend to be in love "Cuando esto nunca fue? / Nomás un casi algo" (When this never was? / Just an almost something). He wasn't her boyfriend; he was her "casi todo" (almost everything), her "casi siempre" (almost always), and now, he's her "ya ni modo" (oh well). He ends things on his own terms, telling her it's her turn to miss what she lost and that he's already deleted her from his life.