It is always told as a fact without explaining the reason. Why do two objects get charged by rubbing? Why one object get negative charge and other get positive charge?
Electrostatics – Why Two Objects Get Charged by Rubbing?
electrostatics
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Charged objects have an electric field in their vicinity. The air will always contain a small number of ionized particles - this can be a result of cosmic radiation, local electrical activity, or just the chemistry of molecules. Now if your comb is positively charged, negatively charged ions will be attracted to it and positive ones will be repelled. Over time, this results in a neutralization of the charge on the comb.
The question then becomes - what is the major contributor to the conductivity of the air? A 1988 research report by Hugh R Carlon, Electrical properties of atmospheric moist air: a systematic, experimental study had the following in its abstract:
All results are consistent with the view that ions are produced in moist air [...]
Reproducing figure 3 from that paper:
you can see that they measured a charge carrier density that is logarithmically dependent on relative humidity - and charge carrier density scales with conductivity (all other things being equal).
This is the reason, incidentally, that most ESD (electrostatic discharge) damage occurs in winter: when the air outside is cold, the relative humidity inside (where it is warm) will be low; thus the conductivity is low, and objects have a chance to build up charge without it leaking away so quickly.
One more figure from the same paper, showing the discharge current measured for different voltages, at different levels of humidity. Once again, it is hard to escape the conclusion that ionization of moisture in the air is responsible for the conductivity (and thus for the discharging of your statically charged comb):
Incidentally, in a dusty environment (see @Boris's answer) you may observe neutral dust particles being attracted to the comb (because of polarization of the particle) - but once it touches, it either sticks, or it will "jump away", having acquired a small amount of charge and therefore being now repelled. In so doing, these particles can be responsible for some charge leakage. But in clean air, moisture is the key component of conductivity.
Because the surface of the plastic wrap is much larger than its thickness, it behaves like a capacitor, accumulating positive charge on one side and negative charge on the other. It creates a potential difference and thus an electric field.
Best Answer
The effect in which two objects get charged by rubbing and remain charged is called the triboelectric effect,
where the root "tribo" means friction in Greek (The Greek word $\tau\rho\iota\beta\omega$ means 'to rub'). Friction is actually unnecessary: contact is enough in principle.
This effect shouldn't be confused with the (Volta or Galvani) "contact potential" between metals which only exists as long as the two metals remain in contact, and especially not with "contact electrification" which was a name of a scientifically incorrect theory of electricity at the end of the 18th century that attempted to overgeneralize the interpretation of the triboelectric effect. "Electrophorus" was a gadget, first produced by Volta, that used the triboelectric effect.
The cause of the triboelectric effect is adhesion - the atoms on the surface literally form chemical bonds. Materials such as fur are ready to lose electrons and become positively charged while the materials such as ebonite or glass gain electrons and become negatively neutral. To get some idea about which atoms are likely to lose or gain electrons, it's useful to know their electronegativity:
The redder atom, the higher electronegativity, and the more likely it is for the atom to gain electrons and become negatively charged. That's especially true for light halogens (fluorine, chlorine) and oxygen. That's partly why glass - with lots of $SiO_2$ - likes to get negatively charged in the triboelectric effect. Even sulfur (40% of ebonite) has a higher electronegativity than e.g. carbon and hydrogen that are abundant in the fur which is why fur loses electrons and becomes positively charged.
Of course, the actual arrangement of the atoms in the molecules matters, too. So this overview of the periodic table was just an analogy, not a reliable way to find out the results of the triboelectric effect.