Non-polarized fixed capacitor
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.
Polarized fixed capacitor
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.
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.
I don't see why you cannot replace them. Just remember that polarized capacitors usually have large capacitance per volume compared to non-polar caps (like ceramic).. so it might be hard to find a non-polar cap with an equivalent value. and as long as the voltage and capacitance matches. Technical speaking it is OK , But say you need to replace one electrolytic 100uF capacitor with non-polarity capacitor. The size of non-polarity one is more than ten times bigger than electrolytic one, and it is far more expensive.
---------- Post added at 12:08 ---------- Previous post was at 12:06 ----------
the usage of polarised or non-polarised capacitor depends on the aplication. One should never apply a negative voltage to a polarised cap lest it will burst/explode/burn. So if your application does not have any situation where the input to the +ve terminal of the polarised cap becomes lesser than its -ve terminal, then either cap can be used.
If there is such a situation, only non-polarised caps should be used