Microwaves are very high frequency radio waves, just like your radio, TV and mobile phone use. The reason they can cook food is that they use a high power which is retained, and concentrated in the cooking area of your microwave (the cavity).
No microwaves are not dangerous unless you were to be exposed to a very high level for a long period of time. Your microwave oven can't "cook your insides" if you stand in front of it.
However people with pacemakers should not stand in close to a microwave while it's cooking as they do give off electrical noise that could upset the operation of a pacemaker.
For those who understand, and who are interested in such detail, the frequency of the radio waves that microwave ovens generate is set by an international agreement at 2,450 MHz (2.45 GHz). They are classified as "non-ionizing radiation" unlike X-rays, Gamma rays and Ultra violet all of which cause harm to us humans by causing cellular damage, and do cause ionization.
The radio waves your microwave generates are almost the same frequency as those used for 3G mobile phones, wi-fi hotspots, bluetooth, and wireless modems. The only proven health hazard associated with microwave ovens is that long term exposure of the eyes to microwave radio waves could cause damage to the cornea of the eye, but it would need to be significantly higher that the maximum (legally permitted) level of microwave leakage from a microwave oven door (5mW per cm2)
The microwaves bounce around inside the cavity, and when they encounter the food they start to make the microscopic droplets of water in the food vibrate, which makes the all the minute particles (molecules) that make up the the food rub together and generate heat through friction (just like rubbing your hands together) .
There is a common myth that microwaves cook from the inside out. Actually they don't, but to take a large potato as an example they generate the heat just below the skin, which then gradually spreads through the food.
Try undercooking a potato (about half cooked), now cut it open. You will find that the outide is cooked fairly well, but the inside is almost raw.
They are created by a device called a magnetron (anyone who has dealt with radar will have heard of these), which is in simple terms a very special type of high power radio valve. They were first made in the 1940's for radar sets, so your microwave is actually based on a technology over 60 years old although the other electronics inside are very modern.
It tells you that instead of a large, heavy transformer inside to step up the mains power to 3000 volts for the magnetron, that your microwave has a lighter, more energy efficient device called an inverter to do the same job.
Another advantage of an inverter microwave is that the microwave cooking power is continuous, unlike ovens with transformers, which means that you can cook with low power for shorter periods of time. (With the transformer type of oven if you set 1 minute on low power you might get no microwave power at all, or full blast for a minute.)
It's a small device inside the oven which senses the amount of steam the food is giving off during cooking to calculate the correct cooking or defrosting time. It works by briefly heating the sensor and taking a background humidity reading for your kitchen, giving the food a short burst of microwaves and then measuring the amount of steam given off by the food. This allows the control unit to calculte the cooking time.