5 Reasons Why It Doesn't Matter How C-3PO Got His Red Arm In Star Wars: The Force Awakens
5. It Was Primarily There To Show The Passage Of Time
The real purpose of Threepio getting a new appendage wasn't some big narrative reason or a particularly lazy version of J.J. Abrams' mystery box, but something much more mundane.
Quite simply, thirty-four years have passed (in-universe at least) since Return Of The Jedi, and in that time things will have changed. But while it was easy to show that with the human characters (damn you ageing) and the vehicle designs, it was a little harder for timeless droids. R2-D2 had an advancement in the form of BB-8 and was out of action for much of the film, so he was simple enough - just add dust - but C-3PO was a little trickier.
The arm was the most simple, striking way to do it - anything else would either be too major (a new face plate) or minor (a leg, although we'll get to that) to have the desired impact - and red stands out while still fitting alongside the gold. If you want to know "why" the character got the arm, that's it.