Why can't we get the same results if is wrapped with a silk cloth for some time? What actually happens when we rub it?
If you left a glass rod wrapped in a silk cloth for "some time" there would be a net transfer of charge.
The difference rubbing makes is accelerates the process due to charge transfer aided by friction
Look up the Triboelectric effect
Materials close together on the series may not experience any charge transfer if simply touched (add friction into it however...) while materials further apart will.
What this also means is two materials that were initially GROUNDED that are then placed in contact with each other & then ungrounded will experience a charge transfer over time.
The rule of thumb is the better the insulator, the great the affinity for charge (there are obviously exceptions - see the chart). Walking on a carpet will generate 35kV of static, sliding down a fibreglass slide will generate 50kV etc...
The friction of rubbing the two is what dislodges electrons from the glass rod - the friction is physically stripping off electrons - which stick to the silk cloth.
The standard tutorial about this can be found here.
This answer on Physics.StackExchange does a good job of expounding on the details of why charge goes to the cloth and not the rod. The Triboelectric Series is essentially the categorization of certain materials' reluctance/admittance to gaining/losing electrons through interactive friction.
The outer electron of some atoms are mobile, meaning they can be removed, or "elevated to a higher energy state." (See the definition of laser for more details on the latter.) Electricity flow is simply the movement of these electrons, loss and gain, repeatedly, across a material. If a material has a net deficiency of electrons, it is said to be "positively" charged. A surplus, "negatively" charged.
If there is a net deficiency at point A and a surplus at point B, and some type of a conductive path is placed between them, then an electric current will flow from B to A, neutralizing the net difference to zero. If there is a charge difference but no flow, then the charge is "static", meaning it's there, but isn't flowing anywhere. Hence, "static electricity."
Learning about static electricity is great for fundamental knowledge of electricity, but electronic circuits don't use this very often. Instead the focus is on that flow of electricity from point B to A, and not how that charge got there or by what means.
Some materials have tightly bound outer electrons. Since these refuse to budge, they do not work like glass and silk do together to form static charge when rubbed. In fact, they pretty much refuse to conduct electricity at all... so are called "insulators." Wax is a good insulator, and so are certain plastics, ceramics, glass, and resins. This is very different from metals, of which most do have loosely bound outer electrons, thus can conduct electricity. This is why metal wires are used as a conductor, with a plastic jacket to "shield" the conductor from accidentally touching some other conductor.