Physical meaning of quantized energy of electron (or n=1,2,3...) in Bohr's model To solve objections on Rutherford's model, one of which is energy deficit, Bohr postulated that the energy of the electron is quantized and $n=1,2,3...$ . But what does this postulate mean physically? Our teacher said that electrons can only circulate on certain orbits, but is this true?
 A: The postulate says that "electrons do not lose energy when they are in the permitted orbits". 
A circular orbit has a different energy according to the radius. Bigger radius = bigger energy.
If you can only have some energies, then only some of the radii are allowed.
That was "new", but it is not a big deal. It's like a shelf: you can only place items on the shelves, but not  in the empty space in the middle. It's weird that this happen in an atom, but it's okay.

This is the physical meaning of what you are asking. How does it "solve" Rutherford's problem? Rutherford predicted that the enelctron would lose energy.
The problem comes when Bohr says "and the electron does not radiate energy while it is there". This, of course, overcomes the problem: it doesn't lose energy, full stop. But wait, how is this?
That's the thing. If you say that the electron can only be in some places, it's acceptable... but how comes it doesn't emmit energy while spinning around?
Our knowledge says that "any accelerated charge emits energy". A circular motion is accelerated, that's basic. So this is breaking a well stated physical law.
Later on, we discovered new things. Quantum mechanics revealed that it works much differently. The electron is not a spinning particle anymore. It is described by a wavefunction that gives the probability of finding the electron there.
A: The physical meaning is that the electron behaves as a standing wave. Standing waves have a condition to be always in phase with itself. For example, a guitar string may have harmonics only with a whole number of half-wavelengths in the length of the string. In the spherical case, you have Spherical Harmonics of different shapes. They define s, p, d, and f sub-orbits of the electron. The in-phase condition of the whole number of half-wavelength makes the orbits discrete (quantized).
Accelerating (e.g. rotating) charges emit energy in quants (photons) and accordingly move to quantized lower energy levels. There is no contradiction here between classical and quantum theories. Both state that accelerating charges lose energy. The essential difference is only in the existence of the lowest orbit. The electron cannot go lower, because a lower orbit would not be long enough to contain the minimum number of the electron wavelengths to form a standing wave. The electron still can fall deeper when it is absorbed by a proton in the nucleus to form a neutron.
So the last question is, why does the electron not emit energy while on the lowest orbit? When we come this far away from the classical theory, we must play by the rules of quantum mechanics and admit that the electron on the lowest orbit does not move with acceleration. The model of the electron "rotating" around the nucleus no longer holds valid. The electron is not "rotating on the orbit", but just "is there on the orbit" as a cloud of a probability distribution with an intrinsic angular momentum (spin). In other words, spin is not rotation.
Also note that charges moving with acceleration do not necessarily emit energy in the classical theory either. It depends on the frame of reference of the observer. See, for example, Paradox of radiation of charged particles in a gravitational field.
