What is so special about speed of light in vacuum? I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get some insight in this subject.
My question is what is so special about $c$? Why only $c$. Its like chicken and egg puzzle for me. Does Einstein reached to $c$ observing light or does he got to light using some number which turned out equal to $c$. 
Why is $c$ not relative. If something has zero rest mass like a photon why they only travel at $c$ in vacuum and not with $c+1$ or $c-1$?
 A: Einstein in 1905 derived $c$ from the Maxwell's equations. Exact title of the paper in which special relativity was published was On the Electrodynamics of Moving Bodies. He essentially just resolved the problem of two electrons moving relative to each other. Moving electrons create a changing magnetic field and at the same time they are accelerated by Lorentz force and electrical force originating from the field.
In an inertial frame of reference associated with any electron there is no magnetic force ($q\mathbf{v}\times\mathbf{B}$, $\mathbf{v}$ being $\mathbf{0}$), only electric field acts on the electron. The solution is: if we change our frame of reference to a frame of reference which is moving at constant speed there is a transfer between magnetic and electric fields. There inherently is a constant in the transformation which units are metres per second. It was called "an Einstein's constant".
Einstein looked at speed of electromagnetic waves calculated using well known at the time magnetic and electric constants (the same formula as for Einstein's constant, by the way), and noted that resemblance with observed speed of light is... intriguing. It was just a suggestion of light being an electromagnetic wave.
So:

*

*Einstein's constant

*speed of light

two separate things. But since light is an electromagnetic wave, it's speed in vacuum is equal to Einstein's constant $c$.
Today commonly we call it just "speed of light" for convenience, but in many contexts it could be called "Einstein's constant".
$$c = \sqrt{\frac{1}{\epsilon_0\mu_0}}$$
A: c is the conversion factor between space (distance) and time, where 3 x 10^8 metres of distance is equal to 1 second of time. 
c is also the maximum speed at which information can travel without causality problems.  That means than all observers must agree on the sequence of events.  There would be a big inconsistency if I pull the trigger of a gun, and the bullet strikes a target; and an observer somewhere, travelling at whatever speed, "measured the bullet to hit the target before I pulled the trigger".  This is equivalent to "c is the conversion factor between space and time" and "Information cannot travel faster than c".
As light photons do not have mass, light travels at c(light) = c. 
So, Special Relativity has nothing to do with the speed of light.  Modern derivations of SR do not use the speed of light to derive the SR equations.
It just so happens that the speed of light is the same value as the c in SR, and that Einstein derived SR in terms of the speed of light.   
If we discovered (we won't, but bear with me) that photons have a tiny mass, light would now travel at very slightly less than c.  We would have to invent a new symbol, c(light), for the speed of light.  But the c in SR (E = mc^2, Lorentz, etc) would remain c as today.  SR would not use the speed of light, c(light).
It is no surprise that all inertial observers measure c to have the same value as c is a property of space-time.  
From Maxwell's Equations, c = the reciprocal of (the square root of (the product of the permittivity, ε0 and the permeability, μ0 of space)).  Permittivity is a measure of the electrical properties of space (vacuum) and permeability is a measure of the magnetic properties of space (vacuum). 
Observers moving relative to each other measure different values for the distance between two events and different values for the times between those two events, but they always measure the same value for the Interval between those two events.  The different distances and times they measure are related because 3 x 10^8 metres of distance is equal to 1 second of time.  
A: Special Relativity is based on the invariance of a quantity called the proper time, $\tau$, which is the time measured by a freely moving (i.e. not accelerated) observer. The proper time is defined by:
$$ c^2d\tau^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 $$
This is similar to Pythagoras' theorem as learned by generations of schoolchildren, except that it includes time (converted to a distance by multiplying by $c$) and it has a mixture of plus and minus signs. The mixture of signs is responsible for all the weird effects like time dilation and length contraction, and because there is a mixture of signs the value of $d\tau^2$ can be positive, negative or zero.
If $d\tau^2$ is less than zero then $d\tau$ must be imaginary, and therefore unphysical. A quick bit of maths will show you that $d\tau^2$ can only be negative if you travel faster than light, and therefore that $c$ is the fastest speed anything in the universe can travel.
So $c$ is special because it determines a fundamental symmetry of the universe.
Footnote:
I've said $c$ is special while Kostya has said the opposite, but actually we are both right.
Kostya is right that there is nothing special about the speed 299,792,458 m/s (though if you change it by much you'll change physics enough that we may not be here :-). However the speed at which light travels is very special because anything travelling at this speed follows a null geodesic, i.e. $d\tau^2 = 0$. This is the sense in I mean that $c$ is special.
A: Nothing. From Nature's perspective speed of light is entirely artificial number.
Imagine that you've discovered an alien culture that measured horizontal length $\ell$ and height $h$ in different units. They live on a planet with very strong gravitational force, and for them it is very difficult to rotate stuff in vertical plane. Such kind of rotations are really unnatural and counter-intuitive for alien-layman. While alien-physicists discovered them and have introduced a special transition coefficient $\alpha$ that transformed one dimension into another, allowing aliens to understand that both of these quantities are just projections of a more general thing called "distance":
$$ d^2 = \alpha^2 h^2 + \ell^2 $$
Then imagine that there is an alien-physics.stackexchange site and someone asked there "What is so special about that $\alpha$?" And the answer is, again, "nothing". Nothing is special about $\alpha$ -- these aliens are just used to special conditions.
Same thing applies to homo sapience -- we are just used to very low speeds, which makes us think that time and space are completely unrelated and cannot be "rotated" into each other. While non-alien-physicists discovered that this is not the case, introducing a transition coefficient $c$...
A: Well one way of looking at it is as follows. 
Imagine that we exist within a 4 dimensional environment, a  Space-Time environment. Now imagine that we have an object that extends across space and that this object is at rest in Space. However, this object is still in motion. It is still in motion across one of those 4 dimensions. It is in motion across the dimension that is known as the dimension of time. 
Now imagine that the magnitude of this motion is equivalent to the speed of which light moves across space (c), and that this specific (c)onstant motion applies to all objects.
No matter what direction any of the objects travel within Space-Time, this specific magnitude of motion is maintained. If a bus turns at a corner, the bus has changed its direction of travel, and thus in turn the bus has rotated. Thus, if any object, as it moves across Space-Time, changes its direction of travel, here too, rotation occurs.
Now, if you take all of this into account and analyze the outcome of such circumstances, you encounter Length contraction, Time dilation, Lorentz Transformation equations, the Velocity addition equation, and the relativity of Simultaneity. 
You also find that under such circumstances you will measure the speed of light as c, and do so no matter what frame of reference the light is being measured from, nor does it matter which direction the light is traveling toward.
