American astronomer Edwin Hubble was the first to notice that the universe is expanding. By "the universe is expanding" I am actually referring to the metric expansion of space.
This means (for reasons currently unknown to us) that space is literally expanding all the time. The average distance between the Earth and any other object in the universe is increasing over time. This has been confirmed by many experiments, but the fundamental cause of metric expansions is currently unknown.
Based on symmetry/randomness arguments, we assume that the Earth is not the very center of the universe. In fact, unless we have evidence to suggest otherwise, we should assume that the Earth just has a random location in the universe.
There is something in the universe called the cosmic microwave background. The cosmic background microwave radiation is basically a weak microwave signal that we can detect by looking at any part of the universe. The reason it exists is because certain theories posit that this type of radiation be released during the big bang once the universe got cool enough---about 380,000 years after the initial big bang, according to the current math. With very powerful telescopes we can measure the cosmic microwave background radiation to a very high degree of precision. Then with a bunch of math we can try to figure out how old the CMB is and how strong it is. This is the oldest light that we can see.
Here's where it gets interesting. We know the universe is expanding. Current evidence suggests that the rate of expansion is increasing. All of the laws you've read about concerning the speed of light being constant does not apply to the metric expansion of the universe. Imagine the universe is a big sphere. That means that if you're sitting on the edge of the sphere trying to look at a light pulse emitted on the other edge of the sphere, if the metric expansion of the universe is increasing faster over the total distance than the speed of light, you'll never be bale to observe the signal.
This is what we mean by the observable universe. The observable universe is what we can see, in principle, base on the metric expansion of the universe. For us the cosmic background radiation is the edge of our observable universe. What's really cool is that the observable universe is shrinking due to metric expansion. There are stars that we can, in theory, see today but won't be able to tomorrow due to metric expansion. The implication is that in many billions of years, if human still exist, space will look a lot bigger and a lot emptier than it does today.
This is sometimes contrasted to the universe at large. This means we could live in a universe where there are things so far from us we'll never see them. Literally, given infinite time, the light would never reach us due to cosmic expansion. Actually, we know this is the case. The universe is so big we'll never be able to see it all.
It's interesting to think of the ancient star systems out there---made of exotic materials, possibly hosting intelligent life---that is part of our universe, and yet we'll never be able to see or interact with.
The size of the actual universe is greater than the observable universe. On of the major questions in physics today is how much they differ. If the observable universe is mostly the size of the actual universe then the distinction is mostly hypothetical. On the other hand, if the actual universe is much larger than the observable universe then it's possible that there are current problems in Physics like baryon assymetry.