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The polarity terminals are on tantalum and electrolytic capacitors. These only work with a DC voltage across them. This is due to their chemical and mechanical nature. If the polarity is reversed they pass high current and explode.
Capacitor is a unilateral device. Those +/- signs are in electrolytic capacitors. This because electrolytic capacitors hold more charge. But how you make them? Most of them have one plate coated with Aluminium Oxide Al2O3 and also act as dielectric between plates.
Now if you have done some chemistry in high school in electrochemical reaction to happen here you would know this plate would become a positive sign of capacitor. Al2O3 most of time because looks like is the cheapest in market.
The reason is charge amount. The capacitor act as "unilateral" device in AC circuit but in DC exibiting (including those called pulsating DC) or pure DC circuits, watch how you connect the polarities.
In AC is not a problem.
It just chemistry forces us to make this stupid concession. In other hand we know the polarity electrolytic caps hold relatively large charge than any capacitor.
Most circuits today are AC, we love AC. Forget Edision with his DC. (kidding of course) In AC we are okay with any kind of capacitor.
In general a capacitor is a bilateral device. However some implementation of the capacitor function (for example electrolitic capacitor) restrict the device to work with a well defined polarity.
actually bilateral or unilateral device, refers to the ability of let the current to flow in only one way or in two ways (forward and backward). So capacitor is a unilateral device in DC circuits and bilateral in AC circuits.
In IC technology, capacitors are not reciprocal
meaning the impedance that you would measure
from one terminal is not equal to impedance of the other terminal because of the parasitics, therefore
it is important to make a distiction between top
plate and bottom plate of the capacitor (which has large associated parasitic cap). Positive and negative terminal also indicate that. And also
for solving the circuit you need to define a reference
right, so this is a 2 terminal component (like resistor)
so you need to identify the difference in between them, so positive and negative
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