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1.A non-polarized ("non polar") capacitor is a type of capacitor that has no implicit polarity -- it can be connected either way in a circuit. Ceramic, mica and some electrolytic capacitors are non-polarized. You'll also sometimes hear people call them "bipolar" capacitors.
2.A polarized ("polar") capacitor is a type of capacitor that have implicit polarity -- it can only be connected one way in a circuit. The positive lead is shown on the schematic (and often on the capacitor) with a little "+" symbol. The negative lead is generally not shown on the schematic, but may be marked on the capacitor with a bar or "-" symbol. Polarized capacitors are generally electrolytics.
Note that you really need to pay attention to correctly hooking a polarized capacitor up (both with respect to polarity, as well as not pushing a capacitor past its rated voltage). If you "push" a polarized capacitor hard enough, it is possible to begin "electrolyzing" the moist electrolyte. Modern electrolytic capacitors usually have a pressure relief vent to prevent catastrophic failure of the aluminum can (but don't bet your eyesight on this).
normally EE stuff show arrows that indicate the flow of electrons (negative to positive) so with this logic the arrow is pointing to the positive terminal!
The only thing I would add is some non-polarized capacitors have a marking showing the "outside foil." The outside foil is normally connected to signal or chassis ground to be used as a shield. I don''t think this is as common as it used to be.