I stuck a 450 V 10 µF capacitor in a 110 AC wall outlet and it exploded... why?
The voltage rating on an electrolytic capacitor is for DC, not AC.  The impedance of a 10 uF capacitor at 60 Hz is 265 ohms so it would draw about 0.45 amps. The combination of too much voltage and too much current will result in destroying the capacitor. In most applications of such capacitors, they follow the output of an AC to DC rectifier so they see an AC ripple voltage on top of a relatively high DC voltage.  The ripple voltage will cause current to flow through the capacitor but it will be much less than what you subjected your capacitor to because the ripple voltage is only a fraction of the full AC input voltage. Most electrolytic capacitors have a maximum ripple current rating to prevent overheating. The voltage rating gives the maximum of DC + AC ripple that the capacitor can withstand. In general this should be derated by at least 25% to protect the capacitor and increase reliability.