To every point of the universe, we can assign an event horizon. It's a spherical surface surrounding these points which travel away from these points at the speed of light. Going backward in time it's obvious that the surfaces shrink to reach an almost zero value near the big bang. The existence of these surfaces (which limits the distance we can observe distant objects, of which there is a majority behind the horizon, which I will explain) is in fact a clue that the universe had a beginning.
The surface came to be when the universe started to expand and had initially a very small radius. When the universe aged the surfaces receded from all points while the universe expanded happily and rather slow. This slow expansion is the reason that although the surfaces are about 13.7 billion years away from us, their spatial distance is not 13.7 billion times the velocity of light (when the distance is given in lightyears) but about three times as large.
Why the majority of astronomical objects finds itself behind the horizon? This is because the universe initially went through a phase of superfast expansion. An expansion on speed, as I read once in a book about the existence of faster than light theories used as an alternative explanation for the effects of inflation, as this super expansion is called. The duration of inflation was extremely short: only $10^{-36}$, more or less. The light could travel only for a short while but had an enormous reach. With the result that the universe became nicely homogeneous (a result which reflects itself in the homogeneous background radiation). The universe grew in this short time into a universe that has a size that is many many bigger than the observable universe. When time passed, more and more of the universe became visible. The horizons grew. Still, the things we see today constitute a small part of the entire universe (the universe is almost flat) and the things behind the horizon will not ever become visible if the surfaces reach a size for which the expansion velocity of the universe relative to the center points of the horizons (us) will become the speed of light.
So initially, the horizons grew. They move away in space due to their velocity through space and due to the expansion of space itself. When the horizons recede back from their center points (or us) at the speed of light, due to the expansion of the universe (i.e., not due to their expansion in space), nothing behind the horizon has a chance of becoming visible.
What about objects on a horizon that is receding at the speed of light due to the expansion of space itself? Well, in that case, the horizons travel away from through space at the speed of light, but the objects further away will travel away from us at a speed higher than the speed of light, due to expansion (which is not to say that something is moving with the speed of light). When the expansion is accelerated, as observations indicate, then objects will move out of this horizon and fewer and fewer objects will stay visible. So, if the Earth and the solar system would still be there in the future, the horizon, although it has grown, will be such that the farthest object we can see is planet Pluto.
If an intermediate observer (traveling at the speed of light) wants to report to us what she has seen, then the moment she arrives our horizon will have grown by exactly such an amount that we can see the same things about which she'll report.
What if the horizon moves away from us at the speed of light due to expansion? Then the situation will be different. The intermediary between us and our horizon will have seen things that we will never be able to see and report to us about these things. Although this effectively broadens our horizon, no information travels faster than the speed of light.