I'm not sure that I'm using the proper terminology here, but essentially microwaves are attuned to the resonance frequency of water molecules, and so make them oscillate rapidly. That's what causes the heat. It's more complicated than that, but someone else can help clear it up for you.
Not quite. Liquid water doesn't have a well-defined resonance and microwave ovens at 2.45 GHz operate well below the peak resonance of water vapor at around 30 GHz. Instead, microwaves heat by a process called dielectric heating, in which polar molecules (in foods, mainly water but also fats and sugars) are tugged back and forth extremely rapidly causing them to bump and slam into neighboring molecules, imparting kinetic energy--heat. Light can heat too--you never burned ants with a magnifying lens as a kid? The problem with light is it doesn't penetrate very far before being entirely absorbed so only the surface gets heated; microwaves can penetrate more deeply, allowing for more thorough cooking. Why 2.45 GHz? At the time these ovens were being invented, nothing really used this band: communications used much lower frequencies and radio astronomy used higher ones so a frequency was chosen that was relatively unused. There's nothing special about it in terms of heating capability. Industrial microwaves used for things like curing glues typically use 915 MHz.