Barajar literally means "to shuffle" (as in cards), but it also means "to consider" or "to weigh options." It's an interesting word because it carries both a literal and a metaphorical sense.
In the context of the song, the lyric "soy hombre y la pienso barajar cada buena historia" (I am a man and I plan to shuffle/consider every good story) suggests the artist is reflecting on his past experiences, perhaps reordering them or carefully considering their meaning, much like one would shuffle a deck of cards to prepare for a new game or consider different strategies.
Grupo Codiciado's "El De Las Calles" tells the story of someone who grew up in the barrio, or neighborhood, and is now reflecting on their past and present. They remember standing on the corner, ready to "tirar bolsitas" [throw little bags] and dealing with "el material que todos quisieran" [the material everyone would want]. It sounds like they were involved in some street activities, but they've moved on.
Now, they're thinking about how they've changed. They're a bit shy, smiling, and they've made a name for themselves, even with "50 artistas" [50 artists] and important people. They decided to "salir de las calles" [get out of the streets] and work hard, like going to Tijuana to "ganar" [earn]. The song acknowledges the struggles of street life, saying "en las calles sí se batalla" [in the streets, you really battle]. But through it all, they've learned and grown, emphasizing that "cada buena historia tiene un guión original" [every good story has an original script]. It's a journey of leaving the past behind and building something new, all while remembering where they came from.