Why broken spacer on Briggs engine output shaft?

If you are referring to the spacer between the end of the shaft and the blade then it broke because the unit struck something and the spacer (also referred to as the blade adapter) broke saving damage to the engine itself. This is a normal occurrence and can be replaced. Check the blade for damage or bending as this will cause the mower to run off balance causing greater damage. Also, I have seen the blade adapter break as well as the flywheel key keeping the unit from starting.