Polarized plugs are a safety feature, especially with something like a lamp.
This connects the "hot" wire to the center connection where the bulb screws
in.

When replacing a light bulb, it is possible you could accidentally touch the
metal ring while unscrewing the bulb. If the metal ring is connected to
neutral (because of the polarized plug), then you will not get shocked.

Also the polarized plug will connect to an appliance on/off switch. So when
the appliance is switched off, it is shutting off the hot. So say something
like a toaster which has a switch which only disconnects one wire. It is
best if the wire the switch is disconnecting is the hot wire! Otherwise hot
would be connected to the heating elements even when the toaster was off,
and a kid might stick a knife or hand inside the toaster, then be shocked.