What's pulmonary edema made of?

Fluid from vessels. Usually a more or less protein rich fluid leaking out of blood vessels in the lungs depending on the cause.
Serum. Cardiac or capillary leak etiologies result in serum accumulation in the lungs in pulmonary edema (greek for swelling). In essence, affected patients are drowning in their own serum when pulmonary edema sets in and can rapidly die or suffer permanent brain damage unless this is emergently and expertly treated with diuretics and cardiotonics while attempts to reverse the inciting cause are underway.
See below. Cardiogenic pulmonary edema is made of fluid backing up from the heart and filling the lungs; non-cardiogenic pulmonary edema is made of inflammatory fluids produced in the lungs in response to infection and many other noxious stimuli.