The alternating electric field causes these polar molecules to oscillate back and forth in an attempt to maintain the proper alignment in the electric field. These oscillations are resisted by other intermolecular forces, and work done by the alternating electric field in overcoming these resistive forces is converted into heat. In other words, the EM waves oscillate at high frequency, and set up currents and move molecules. The moving molecules and current generate heat. It has nothing to do with excitation.
Water is a polar molecule and has good heat transfer, so it is a good microwave-able material.
Many biological molecules area also polar. The microwaves penetrates most materials to a depth of 1-2 cm. The heat is then transferred by conduction to the whole of the material.