You've actually got a few questions involved here, dmakfan.
First, in a "live sound" situation, monitors are generally referring to the speakers that the band uses to listen to themselves. Whereas in a studio, monitors are used to refer to the speakers the engineer uses to preview the mix. Generally, although both are called "monitors", we are talking about two different types of beast.
Nearfield monitors are a specific type of studio monitor, which are designed to be listened to in relatively close proximity (near, get it).
Powered monitors (usually found in studio applications) are monitors that have an amplifier built into them. Essentially there is no difference between a pair of powered monitors, versus unpowered monitors with an amp (except that in the latter the amp is a seperate component). The (supposed) advantage of powered monitors is that the manufacturer has specifically designed the amp to work with their speakers - so some of the guesswork of matching components is taken out of the buyer's hands. (There are also bi-amped and tri-amped speakers, but I'll leave that for another time.)
Lastly, feedback (which is why I began this by talking about live sound). Feedback is simply the situation where sound coming from a speaker is picked up by a live microphone and then is sent through the PA where it is reamplified again (and again picked up by the microphone and reamplified, and so on, and so on). Most normally this will occur at a specified frequency, due to the fact that loudspeakers do not handle all sound frequencies evenly. If you had a perfectly flat speaker, you would get feedback at all frequencies at exactly the same time.
Generally monitor speakers used in live situations face the back of the microphone and are angled up toward the band. This design helps to direct the sound away from the input side of the microphone, and therefore help control the feedback. EQ in the sound system can also help to control feedback, since you can cut back on the particular offensive frequency.
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