Light travels at this speed because it is propagated by a massless particle, the photon. It follows that it travels at the universal speed $c$ which is always observed to be the same from all frames of reference.
Why is this? We can partly answer this question by making basic symmetry and homogeneity arguments about our universe and then one can derive the form of all possible co-ordinate transformations for the relativity of inertial frames that are consistent with these basic symmetries and homogeneities.
To understand how this is done, see the section "From Group Postulates" on the Wikipedia Page "Lorentz Transformation". (Also see my summary here).
Now it so happens that Galilean relativity is consistent with these basic assumptions, but not uniquely so: the other possibility is that there is some speed $c$ characterizing relativity such that $c$ is the same when measured from all frames of reference. Time dilation, Lorentz-Fitzgerald contraction and the impossibility of accelerating a massive particle to $c$ are all simple consequences of these other possible, non-Galilean relativities.
So we have two possibilites: infinite $c$, which is equivalent to Galilean relativity, or a finite $c$. We know that we live in a universe with the latter relativity, because we have observed a speed, namely that of light, that is the same in all reference frames. Then the relativity that follows assuming a $c$ with the value of the speed of light has correctly foretold all experimental tests. It is a highly falsifiable proposition, but it has withstood all experimental attempts to falsify it.
So why is $c$ not infinite? This is simply an experimental fact as far as I know, (which is roughly to a basic working knowledge of General Relativity). There is no basic underlying reason why we have a finite $c$ and not Galilean relativity aside from that the latter is patently falsified by experiment and the former is not.
One consequence of a finite $c$ is that it stops a causal chain of events spread throughout space from happenning all at once. An infinite $c$ would mean that events here on Earth could provoke other events instantly in the middle of M87, and this is not what is observed to happen.