Compi is a cute, colloquial slang word for "buddy" or "pal" in Spanish. It's a shortened, more informal version of the word compañero (companion).
In the song, Alvaro Soler promises, "ser tu compi en cielo azul y en tempestad" (to be your buddy in blue skies and in storms). Using this word instead of a more formal one like amigo or compañero adds a layer of warmth and deep friendship to the romantic promise, making it extra special.
This song is a super sweet declaration of love from Spanish singer Alvaro Soler. He sings about finally finding the person he's always dreamed of. He starts by wondering how he found her "Entre ocho mil millones" [Among eight billion people], deciding it must be a mix of luck and not losing faith. He feels like he was lost, traveling between planets, and just happened to land on hers, staying without a second thought. His world, once "en blanco y negro" [in black and white], is now full of color because of her.
The whole chorus is built around the idea that she is exactly the person he imagined. He dreamed of "Desayunando besos en la cama" [Having kisses for breakfast in bed] and waking up next to her every day. He even imagined their arguments would be playful pillow fights! He loves her natural beauty, telling her she's even more beautiful "recién levantada" [just woken up] than with makeup on. It's a song about a dream coming true and wanting to build a life together, promising to be her "compi en cielo azul y en tempestad" [buddy in blue skies and in storms].