Steel casting and machining parts for rocker arm used in automotive

What is the purpose of the rocker arm?

The rocker arm (in the context of automotive, marine, motorcycle, and reciprocating aero engines) is a swing rod that transmits the radial motion of the cam lobe to the linear motion at the poppet to open the poppet.

How did the rocker arm break?

Weak valve spring or drooping spring will cause the rocker arm to be slapped by the cam when the cam convex angle rotates. There may be a stuck / warped stem, in which case the rocker can break daily if the valve decides to keep closed, the cam forces the rocker to open it.