due to polarization under changing electric field water molecules start rotate and give some energy to other molecules in solution resulting in increasing of system energy (sorry my formulations I'm biologist ;)
Microwaves act as high frequency electric fields and will generally heat any material containing mobile electric charges, such as polar molecules in a solvent or conducting ions in a solid. Polar solvents are heated as their component molecules are forced to rotate with the field and lose energy in collisions. Semiconducting and conducting samples heat when ions or electrons within them form an electric current and energy is lost due to the electrical resistance of the material.
Conventional heating usually involves the use of a furnace or oil bath, which heats the walls of the reactor by convection or conduction. The core of the sample takes much longer to achieve the target temperature.
Microwave heating is able to heat the target compounds without heating the entire furnace or oil bath, which saves time and energy. It is also able to heat sufficiently thin objects throughout their volume (instead of through its outer surface), in theory producing more uniform heating. However, due to the design of most microwave ovens and to uneven absorption by the object being heated, the microwave field is usually non-uniform and localized superheating occurs.
Different compounds convert microwave radiation to heat by different amounts. This selectivity allows some parts of the object being heated to heat more quickly or more slowly than others (particularly the reaction vessel).
Microwave energy causes electrons in molecular dipoles to be excited but they cannot follow the fast electric field so they give up the added energy to dipolar rotation. The greater the loss modulus of the material, the greater the rotational effect. Only metals of the thickness of their skin effect will absorb in microwaves; thicker and they reflect; thinner and they transmit. Because there are no dipoles in glass, ceramics, and air, the only heating occurs in the molecules with dipoles. Adhesives for example react very efficiently even though the air, oven, and fixtures are not heated. Also because the reaction sites are usually dipoles, the overall temperature of the reaction is much lower.
It is also possible to have no arcing of metals and to have a very uniform microwave field if a variable frequiency system is used. This allows practical curing of even very complex electronic systems to be manufactured with microwaves at lower temperatures and lower stress. Lower crosslink density is another benefit in polymers.
Another way to look at the speed of microwave heating is through the collision version of the Arrhenius equation:
k = Z p e^ (Ea/RT)
where Z is the collision frequency, p (rho) is the productive collisions, Ea is the energy of activation, R is the universal gas constant, and T is temperature.
There are many more collisions with rotating as well as translating molecules and there are statistically more productive collisions.
Note that even parts of the molecules that do not have dipoles still have clouds of polarizable electrons that will respond to microwave excitation. Microwaves do not produce enough energy to break covalent bonds but they will force even non-polar sections of organic chains to rotate. This effect is clearly evident in the high mobility of the "infinite polymer" backbone of gelled thermosets that maintain kinetic activity beyond the usual transition to a Hookean solid. This allows lower temperature curing and the prevention of vitrification. See J. Appl. Polym. Sci., August, 2016.