This is the part of the microwave that produces the microwaves needed to heat the food and ingredients inside the appliance. The high voltage diode, high voltage capacitor, and transformer work together to transform AC current to DC, at which point the magnetron is activated, and the heating action of the device is set in motion.
Unfortunately, complex parts like a magnetron cannot be repaired. You can check if this is the cause of the problem by using your multimeter to see if it is functioning. While testing the terminals that lead to the magnetron, you should get a reading of less than 1 ohm. Anything other than this, and you have enough evidence to halt your investigation and order a new component. That said, it might be even cheaper (and is definitely the easy option) to get yourself a new microwave outright. A typical magnetron can cost anything from $100 to more than $200 - typically around the same price as a basic microwave.