Some 13.7 billion years have passed since the Big Bang. That means that 13.7 billion years ago, everything (Every Thing) was stuck together in a singularity. According to the way people thought when the notion of a Big Bang was first accepted, the furthest away two objects could be from each other now (in the visible universe) is 13.7 billion lightyears, on the basis that the "cosmic speed limit", aka the speed of light, means that the furthest you can go in a year is one lightyear.
And then redshift measurements showed the universe is quite a lot bigger than that.
Some years back, I was teaching Computer Stuff to a bunch of code ninjas with brains the size of Jupiter, all of them smart enough to get physics jokes. So at one point, I gave a little ten-second riff on inflation theory:
According to relativity theory, nothing can travel faster than the speed of light. And according to inflation theory, that's exactly what the nothing did.
To my surprise, one of the guys said he'd puzzled over cosmic inflation as a physics student, and I'd just made it totally clear! (I'd thought I was merely being a smart-arse to relax the mood for a moment.)
In case you don't know about this stuff already, the point of inflation is that it's the spacetime-stuff itself that expanded. Lightspeed is the speed limit for anything travelling inside the medium that is spacetime; the medium itself can expand as fast it likes.
I grokked this early on because I'd previously been puzzled by explanations of cosmic redshift that refer to it as the Doppler effect. It really isn't. The equation for the wavelength/frequency shift is the same, but the model is different: the sound of a train approaching and then receding changes in pitch because of the motion of the train. Cosmic redshift is due to the expansion of spacetime itself, not the motion of stars through spacetime. Very, very different.
And of course, I mention it now because of the strongly named BICEP2 experiment at the South Pole that's discovered polarisation in the cosmic microwave background radiation that seems to be the "footprint" left by cosmic inflation when the universe was brand new.
On the other hand, the effect is rather stronger than predicted (originally by theoretical physicist Leonid Grishchuk at Cardiff University, Cardiff being one of the BICEP2 participants). Hope that doesn't mean it's like those little espresso neutrinos sniffing the Italian CERN coffee and breaking the speed limit except that they really weren't...