What makes waves propagate? Why do electromagnetic waves propagate?
I have searched a lot about EM waves, but I am still unable to understand  what is driving them. Could you explain?
 A: It is tempting to think that if something is moving there must be a force that keeps it moving. However ever since Newton formulated his first law of motion we know this isn't the case. An object, whether it's a massive object or a light ray, will carry on moving at a constant velocity unless some force acts on it. So nothing is needed to keep the light ray moving.
But light is a bit special because it can only travel at the speed of light, while of course massive objects can travel at any speed up to (but not including) $c$, and it's perfectly reasonable to ask why this is. And I'm afraid I don't have an intuitive answer for you. Classically we describe the electromagnetic field using Maxwell's equations. Light is an oscillation in the electromagnetic field, and if we do the sums to find out what speed this oscillation travels we find the answer is $c$. Strictly speaking we find the velocity is:
$$ c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}} $$
where $\varepsilon_0$ and $\mu_0$ are constants. Why $\varepsilon_0$ and $\mu_0$ have the values they do we can't say - that's just the way our universe is built.
At the risk of misleading you: sound waves in air travel at 340 m/sec but we don't find this constant speed odd. The speed is related to the elasticity of the air and the sound waves can't travel at any other speed. Now the electromagnetic field isn't a medium like air, but the same principle applies. You can think of the speed of light as being a result of the elasticity of the electromagnetic field.
A: According to maxwell's electromagnetism, a changing magnetic field gives rise to electric field, and a changing electric field gives rise to magnetic field lines.. 
So simply put, when a changing field of either type(electric or magnetic) is produced it gives rise to its counter parts (magnetic and electric)..
So once a changing field comes to existance repeated process of regenerating the electric and magnetic field comes to picture which results in the propagation of EM waves(which once emitted propagate independently with any dependance on its source)
A: Maxwell's equations of electromagnetism don't allow an electromagnetic wave to just sit there without moving in empty space (in the absence of electric charges).  An electric field is created by a magnetic field changing in time, and vice versa, so the coupled fields have to be changing in time (i.e. propagating) in order to exist and sustain themselves.
