Correrías translates to "adventures" or "escapades." It's a charming and slightly old-fashioned word that evokes a sense of youthful fun and memorable experiences.
In the song, Diomedes Díaz mentions his father "Recordando viejos tiempos / De sus bellas correrías" (Remembering old times / Of his beautiful escapades). It paints a picture of a father who lived a full life, full of interesting stories and perhaps a bit of mischief, making it an endearing and unique word choice.
Diomedes Díaz opens by saying exactly what he's doing: "Voy a componer un merengue" [I'm going to write a song], and who it's for: "Pa' cantárselo a papá" [to sing it to dad]. He places his father on a real map, a farm in Carrizal close to La Junta, and gives him credit for his own body and his career in the same breath. "Me dio el tamaño que tengo" [He gave me the size I have], he sings, then later: "Pero todo esto se debe / Al ejemplo de my viejo" [But all of this comes from my old man's example].
Midway through, the song turns into a prayer. "Pero la Virgen María / Me lo tiene que cuidar" [But the Virgin Mary has to take care of him for me], he asks, wanting his father to "vivir tranquilo" [live in peace] and stop worrying about him. By the final verses he brings his mother into it too: "La que lo ha sabido cuidar / Hace mas de treinta años" [The one who has known how to take care of him, for more than thirty years]. A song that starts as a gift to one parent ends up thanking both of them, still together on the same farm.