The Universe is expanding – that is, all the galaxies in the Universe are moving away from each other. The rate of expansion is not constant however. Gravity acts to slow down the rate of expansion (though recent evidence suggests the rate of expansion may in fact be speeding up. Gravity is not the only factor at work). If the force of gravity is strong enough, all the galaxies will slow down and eventually start moving towards each other. Whether or not the force of gravity is strong enough depends on how much matter there is in the Universe and how thinly it is spread – its density in other words. If the density of the Universe is high then the Universe will stop expanding one day and the galaxies will start moving towards each other. There will be a 'Big Cruch'. Conversely if the density of the Universe is low then the galaxies will kepp moving away from each other forever. The Universe will expand forever.
Between these two possibilities there is a third: the Universe will continue to expand forever but the rate of expansion will continuously slow. If the Universe were any denser, it would eventually stop and start to contract. Any less dense and it would expand forever more quickly. There is a critical density
which defines the boundary between these last two.
The critical density depends on the strength of gravity as defined by the Universal gravitaional constant,
and on Hubble's constant
which is a measure of the speed of the galaxies away from each other: 
With
we have
This is a very small density, less than six hydrogen atoms per cubic meter, but our best estimates of the density of the Universe give a density very close to this critical value. There is no inherent reason for the density to be so close, and in a sort of 'since it is so close to the critical value it must be equal to it' sort of argument, many astronomers think it is equal to the critical value and the Universe is flat. It may be surprising that our calculations of the density of the Universe are so small, since on Earth matter is all around us, but actually most of the Universe is empty space, consisting of the empty space between galaxies. The spaces between galaxies are vast and in these empty spaces there is very little matter at all.