Generally when people talk about a broken wrist they mean the end of the radius bone closest to the hand. This is one of the most commonly broken bones in the body. The vast majority of distal radius fractures can be safely managed in a plaster cast. Some, if they are not displaced, don't event need a plaster cast and can be managed in a splint.
However, some displaced fractures could lead to a painful and stiff wrist in the future, if they are not put back into position and held with metalwork. There are different devices that can hold the fracture in position, but most hand surgeon would use a plate made out of titanium or stainless steel.
Factors that might lead to your surgeon recommending surgery include a fracture that goes into the wrist joint, a very tilted fracture, or a very shortened fracture.
For more information, or to get in touch about your fracture, see:-
https://rupertwharton.com/pages/wrist-fractures
https://rupertwharton.com/pages/contact
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Rupert Wharton, Hand surgeon in Central London (King Edward VII) and South West London (New Victoria and Kingston Private Health)