The two basic microwave heating mechanisms – at molecular level
There are two heating mechanisms in substances containing water,such as foods. The same mechanisms exist also in many other so-called polar liquids such as alcohols and ketones.
The first heating mechanism is caused by the molecules in a polar liquid “hooking on” each other due to the uneven charge distribution of the molecule, so that one end gets an excess of  positive charge and the other a negative charge – see the picture to the right which shows water molecule groups. The microwave field (+ and – and downwards directed arrows in the picture) will then exert a turning force on the molecules – they attempt to align with the field and energy is supplied to them. When the field direction changes (this occurs 4,9 billion times per second at 2450 MHz), the molecules return the alignment energy to the field – the system behaves like an electric capacitor connected to an alternating voltage. If the microwave frequency is very high, the molecule groups will however rotate so sluggishly (in relative terms) that they do not at all align with the field – no energy transfer takes place. In a certain frequency interval, the molecule groups will (statistically) still rotate but with some lag, which depends on their mass inertia. All energy will then not be recovered when the field direction is reversed. A part will instead be permanently given off to the molecule groups, which will heat up by a general net increase in their movement. The phenomenon is called dipole relaxation.
For water, the maximum absorption capability at room temperaure is at about 20 000 MHz. The capability is “suitable” at 2450 MHz, i.e. sucessive microwave absorption occurs down to about a depth of 20 mm in materials with a high water content. The capability also depends on the temperature and decreases when it rises, since the number of molecules hooking on to each other is reduced with increasing general, incessant movement (so-called Brownian motion).
The two movie images below the top illustration shows what does not happen with microwaves. Simple rotation cannot occur due to the high collision rate.The flexing shown to the right occurs in individual molecules exposed to infrared radiation with 1…5 µm wavelength, and is the cause of the blue colour of water. The left image is from this excellent “water site”, and the right from the Peter Püschner industrial microwave site.

The other heating mechanism results from many liquids (e.g. water) being able to dissolve salts, acids and bases which then become dissociated into charged ions.The ions are influenced by an electric field causing a net movement in its direction – see the image to the right, which shows a negative ion (e.g. the chloride ion in common salt) and a positive ion (e.g. sodium).
That the ions get an additional net movement is equal to a temperature increase, by the lectric energy being converted into heat. This effect is frequency independent.The ionic (or electrolytic) conductivity measured at low frequency can directly be recalculated into a part of the microwave absorption capability. This increases with increasing temparature, since the shielding by adjacent water molecule groups diminishes with increasing temperature  – the ions become more “naked”.
The mechanism described here is called ionic conductivity.
In common food substances, the two mechanisms contribute about equally to the overall microwave absorption capability, in spite of the salt content typically being about 0,6 % or less. There is also a favourable compensation by opposite temperature depencences of the two mechanisms. – A diagram showing this: (high resolution PNG; simpler PDF).   Other material data and a description of the penetration depth concept. Read here about the two other heating mechanisms and why microwaves “only” heat up substances.