I can see that there are speakers of various sizes with various power ratings. However, they usually seem to be 8 ohm or 12 ohm. What does this refer to? And why are they created to be this way? I mean why do 7 ohm or 10 ohm not exist?
They are usually that way, partly for standards, partly for physics. From a standards perspective, it helps to have a particular set of impedances for which you can design amplifiers for, knowing the load is important in designing one. From a physics standpoint, the impedance of an audio driver is largely determined by its mechanical resonance. Not only is the impedance frequency based, but in speakers the impedance tends to be it's lowest (excluding DC signals) around its resonant frequency, I believe just slightly after resonance. As a related aside, speakers are composed of drivers and those drivers are connected to the amplifier by a crossover network. This networks purpose is to separate the signal frequencies into the appropriate driver, and ideally, present a nicer load to the amplifier as well.