The radius is one of two bones in the arm, and distal simply refers to the wrist end as opposed to the elbow end.
This past season, Albert Pujols suffered a distal radial fracture, and faced with a diagnosis that he would miss 4-6 weeks, (some experts suggested he would need more time), returned to the field in a mere two and a half. The man is a machine.
In other mortals, wrist injuries tend to linger and sap a player's power. There's never really a good time to break a wrist, but Marte should have plenty of time for a full recovery coming off a statistically impressive showing in the Fall League.