To heat a substance, the material must couple to the microwaves. In other words, the substance must absorb electromagnetic energy.

Generally speaking, two mechanisms are available: 

Dipole Rotation

This is the case with materials which have a pronounced dipole (water, acids, solvents). In the rapidly changing electric field, the molecules try to orient themselves in the direction of the field lines. This sets them in rotation-vibration. The energy absorption from the microwave field is more intensive the closer the resonance frequency of the molecule is to the frequency of the microwave.

Dipole
Moments

Ionic
Conduction

Heating in the electromagnetic field also occurs when there are free ions (electrolytes, glassy materials and ceramic materials). 

Both mechanisms, dipole rotation and ionic conductance, are influenced by various factors:

• Wavelength 
  
• Physical properties of the solution
• Dielectric constant 
• Polarity 
• Temperature 
• Viscosity 
• Thermal capacity
  
• Ion characteristics (ionic conduction) 
  • Size 
  • Concentration 
  • Charge 
  • Mobility