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Most electrolytic capacitors are polarized and require one of the electrodes to be positive relative to the other; they may catastrophically fail if voltage is reversed. This is because a reverse-bias voltage above 1 to 1.5 V will destroy the center layer of dielectric material by electro-chemical reduction.
Following the loss of the dielectric material, the capacitor will short circuit, and with sufficient short circuit current, the electrolyte will rapidly heat up and either leak or cause the capacitor to burst.
An electrolytic can withstand a reverse bias for a short period, but will conduct significant current and not act as a very good capacitor. Most will survive with no reverse DC bias or with only AC voltage, but circuits should be designed so that there is not a constant reverse bias for any significant amount of time.
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