About 14 billion years ago the universe came into existence with the Big Bang. Early in process the universe was too hot for matter to form and the was a fairly uniform “glow”. As the universe expanded it cooled. You can think of compressed gas in a can being released, like spray paint or cooking spray, as the gas expands it cools off. After a while things cooled down so that matter could start forming.
But that “glow” is still around. It too has cooled off, to just a few degrees, but it comes from everywhere as its discovery was some of the first, best, evidence for the Big Bang. That “glow” is called the cosmic microwave background radiation (CMB). But if the “glow” was uniform then how dis we end up with matter clumping into stuff. Well NASA put up a couple observatories and showed that the CMB actually had some variation in it.
The Big Bang is well accepted as what happened. But there are always details to work out. Back in the 70s it was noticed that there were problems with the Big Bang. Some of the things that were predicted, weren't found. So an addition to the Big Bang theory was made. That was of “inflation”. Not the other kind of inflation that was big in the 70s, but a theory that shortly after the Big Bang, (and I do mean shortly 10-32 seconds after, and that's small) the universe had a short period where it expanded quickly (faster than the speed of light).
While inflation did help explain some things, science grows by confirming predictions. And one of the predictions that were made about inflation was that gravitational waves would have caused a certain type of polarization of the CMB. These predictions were made years ago (back in the 80s).
Well, just recently BICEP2, a special telescope built down near the South Pole, released a report where the polarization was confirmed. This has provided good evidence for the hypothesis that this period of inflation occurred shortly after the Big Bang happened.
And that's the way science is supposed to work. People come up with a hypothesis and from that hypothesis they make predictions. Things that can be measured. At least in theory. Sometimes you have to wait a while before technology catches up so the devices can be built that can measure the effect that was predicted. But then you or other scientists make the measurements and determine if the predictions were true or not.
And if the predictions were found to be true, then the hypothesis gets some confirming evidence. And once enough evidence is found that the not believing that the hypothesis is true is silly, the hypothesis graduates up to a scientific theory. Which unlike the vernacular is a pretty prestigious class of scientific ideas. (In science, saying “It's just a theory” is a good way to get you laughed at. You're not using the word the way scientists do.)
So right now, we might still be wondering about the wacky idea of cosmic inflation. But for now the scientists that hypothesized it have some evidence to back them up. I think I can hear them saying “Bazinga” right now.