That is the compressor start relay and klixon. This happens most of the time when a unit os several years old due to the contacs on the relay and klixon getting loose from heat which causes more heat and then results in a failure. It can also happen when the compressor itself fails to start due to a failure of the compressor. The Klixon is a tthermal protector that controls a start winding period It heats up and then opens the circuit if the compressor does not start.

You did not mention any symptoms prior to your discovering the burnt electrical module so I am assuming there were none visible inside or out.

It is worth the effort to have this checked out by a qualified repairman. Many times it is as simple as replacing the start realy and klixon (interlocked as an assy when installed) Other than the service call and labor the parts required to attemot repair of this unit are less than $50.00. Once again it is worth an initial attempt at repair if the unit is less than 8 years old.