There is an analogy between the expansion of the Universe and shooting something up into the air. If you throw something up, it will normally fall back to the group -- what goes up, must come down, right? Normally true, but we also know that if we shoot something up in the air with enough force, it will go out into space -- like the spacecraft we have sent into space, and which are continuing on their merry way out of the Solar System. And we also know that if we shoot something up in the air with just the right amount of force, it will go into orbit around the Earth -- a little less force and it will fall back to Earth; a little more force and it will go off into space, but with just the right amount of force it will circle the Earth.
In the same way, there are three broad possibilities for the fate of the Universe. Either it is flying apart so quickly that the gravitational forces of everything in it will never overcome the velocity, and it will continue to fly apart forever, or it is flying apart so weakly that sooner or later the gravitational forces within will take over and everything will end up flying back together some day in what's called a "Big Crunch". Then there is the so-called "critical density", where there is "just enough" stuff to slow down the expansion of the Universe, but not quite enough to make it all collapse back together. We think the Universe is very close to this critical density.
How much stuff is this? Given how fast the Universe is expanding, it turns out that this critical density is about 10-26 kg/m3. That is, one one-hundredth of a trillionth of a trillionth of a kilogram per square meter. This is small, but how small, exactly? It turns out that this is about the the mass of about six atoms of the Hydrogen, the lightest element (per particle). So, we're saying that on average, the Universe has a density about about six Hydrogen atoms per cubic meter. Given that you're probably less than a cubic meter in volume, and you have many, many, many more atoms than this, we see that the Universe is not very dense at all.
For a more numerical comparison, water on the Earth is about one hundred thousand trillion trillion times denser than this average Universal density.
As an aside, I should emphasize that the density given above for the Universe actually includes things other than the atoms we're used to thinking about -- that is, it includes dark matter and dark energy. It turns out that the "normal" stuff in the Universe is only about five percent of the total. So the density of "normal" things we're used to thinking about is actually twenty times less dense still!