How exactly charges apply force on each other from distance? How come the two charged bodies attract or repel each other ?
When we remove the other body the interaction disappears so what exactly a charged body do to attract or repel another one (it is not even touching the other one)
How can something interact with another without even touching it?
 A: You are intuitively thinking about interactions between two charges as if they would need to reach out and touch each other to interact.
It is very important to understand that both charges in this case create something we call a static EM field.

An electromagnetic field (also EM field) is a classical (i.e. non-quantum) field produced by moving electric charges.[1] It is the field described by classical electrodynamics and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics.

https://en.wikipedia.org/wiki/Electromagnetic_field
In reality, we do not know how these static EM fields affect other particles, we just describe this phenomenon by using virtual photons. These virtual photons are not real, they are just a mathematical tool to describe the effects of the static EM field.
In the experiments, we see that this effect is real, and that these static EM fields somehow (without classically touching each other) effect other particles, and when we mathematically try to model this phenomenon, we use these virtual particles.
This is where the classical intuition does not work anymore, imagining that the charges need a hand to reach out and repel or attract each other, but the nature of the universe is so, that these charges somehow create a static EM field around themselves, and using these static EM fields, you could say that they actually can reach out and attract or repel each other.
A: Charge is a property that a body can possess. This charge gives rise to a field in space known as an electrostatic field. If the charge is moving, a magnetic field coexists and a electromagnetic field is created. When you bring another charged body into this field, it will interact with the field and experience the Lorentz Force (why and how this happens can only be explained with quantum mechanics). Hence we generalise by stating that charged body exert force other charged bodies. 
The same can also be said for two masses experiencing Gravitational Force. This however cannot be explained by quantum mechanics but rather with special relativity. A framework which describes both really well is  yet to be found.
