Colarme comes from the verb colarse, which means 'to sneak in' or 'to slip into'. It's a less common, more evocative verb than simply 'to enter'.
In the song, the singer expresses a deep desire to "colarme entre tus sueños" (sneak into your dreams). This phrase beautifully conveys his longing to be closer to the person he loves, to enter their most private thoughts and spaces, and to confess his feelings in a way he can't when they are awake. It adds a layer of intimacy and vulnerability to his confession.
Andrés Cepeda spends this song admitting something he's ashamed of. "Qué difícil es amar" [How hard it is to love], he starts, describing himself betting everything on cards hidden under the table. He's the storm next to her calm, sneaking into her dreams at night to say what he can't say to her awake: "Quisiera colarme entre tus sueños" [I'd like to sneak into your dreams].
The chorus lays out exactly what he did wrong. "Porque tus besos" [Because your kisses], "Los gasté en alguien más" [I wasted them on someone else], he admits, and no apology fixes that. He can't shake her either: "Tus labios nunca lograré dejar atrás" [Your lips I'll never manage to leave behind]. By the end he isn't defending himself anymore, just stating what's underneath all of it: he loves her more than he knows what to do with.