The reason a device can draw a higher current than it's rated to draw is power factor. Many devices are inductive (or very occasionally capacitive) loads and as a result a significant amount of current flows between the device and the supply just to charge and discharge the inductors (or capacitors) as the a.c. waveform varies. This current flow doesn't do actual work, it just heats up your conductors and wastes energy.
If you worked out the current that should flow based on the "real power" in watts, you would have I = P/V= 1200W / 110V = 10.91A
However as this device (and most other devices too) has a less-than-unity power factor, the equation for power is actually P=V x I x p.f, and current is I=P/(V x p.f), where p.f. will be less than one so the current flowing will be higher than the 11A we need to get 1200W of "real power"
In your case, if it's drawing 18.9A then we can see p.f. = P / (V x I) = 1200/(110x18.9) = 0.58. This is pretty poor, but as I understand it not uncommon for microwaves.
So your microwave has an "apparent" power of 110V * 18.9A = 2.079 kVA (this is what is "apparent" when you measure the current draw using a meter), but only delivers 110V * 18.9A * 0.58 = 1205W of heating to your food (the power doing "real" or useful work)