Propagation of EM waves When we say that electromagnetic waves propagate through space and time. What is the quantity that is actually travelling. We say that electric and magnetic fields are perpendicular to each other and to the Direction of propagation of waves. But they are not physical quantities. So what travels from one place to other that leads to the propagation of electromagnetic waves?
 A: The waveforms that define the shapes of the electric and magnetic fields travel through space at the propagation speed, c, along with electromagnetic energy. 
An analogy--Think of waves traveling in water: the water molecules only move up and down but the wave shape travels along with its peaks and troughs moving at the propagation velocity.
In the process of doing this energy is transferred from the molecules at one position to the adjacent molecules in the direction of propagation--and so on...
A: Nothing travels from one point to another in any wave, based on my interpretation of your statements.  Electric and Magnetic fields are as real as the test particles they act on in the limit as those test particles are made to vanish.  E = lim(F/q) as q-->0.  In the field paradigm, these vectors exist in all of space when some source is present.  In a static situation they do not move from one place to another, but cause test particles to move in their presence due to the Lorentz force.  If something causes a "jitter" in the field at some point, say the oscillation of a source charge or sudden change in current in a circuit, then a sort of chain reaction occurs due to Faraday's law of induction.  A change in magnetic field strength or direction causes an Electric field to be set up in response to that change.  A change in electric field strength or direction causes a magnetic field to be set up in response to the change.  If one thing changes then this reaction occurs from one point to the next and travels through space.  If the source is periodic, i.e. is forced into simple harmonic motion, then the disturbance produced will grow and shrink at the same frequency of oscillation as the source.  This is due to linearity of the equations that govern classical electrodynamics in vacuum.   
A: 
When we say that electromagnetic waves propagate through space and time. What is the quantity that is actually traveling?

Electromagnetic radiation consists of photons, emitted by excited subatomic particles. After being emitted, photons propagate through empty space as indivisible quanta at the speed of light. Photons can carry very different energy contents, this is the quality you ask for.

We say that electric and magnetic fields are perpendicular to each other and to the direction of propagation of waves. But they are not physical quantities. So what travels from one place to other that leads to the propagation of electromagnetic waves?

Both field components oscillate from the maximum energy content to zero and then - with opposite signs - back to the maximum. The frequency of these oscillations is around 300 terahertz.
One remark
It is said that electric and magnetic fields from a source spread out to infinity. For an oscillating source (with $10^{12}$ Hz or even with 1 Hz) this it unimaginable. Quantum mechanics defines an overall existing electromagnetic field and treats the fields of any electrical or magnetic source as excitation of this EM field. It is my personal conviction that the oscillating fields of the photon can thus be regarded as spatially limited. The photon then moves like a bubble with an oscillating contour.
