Скачать или смотреть Why does polarity capacitor blast when you reverse the voltage ?

First of all, let's see how does this electrolytic capacitor actually work. These kinds of capacitors use oxide layer as a dielectric. So while manufacturing, an anode is made as the metal (which is capable of anodizing and producing an oxide layer ) and cathode may be a solid electrolyte and it covers the oxide layer.

Take aluminum capacitors for instance. This uses a thin aluminum foil as anode and Aluminium borate as a cathode. When +ve potential is applied to the anode, oxidation occurs and a thin layer of Al2O3 (aluminum oxide) is formed which serves as a dielectric. Hence you get very good capacitance.

If you change the polarity, then cathode and anode get changed so it breaks the oxide layer and short circuits the capacitor which ultimately blasts with a 'pop' sound.