If the mass in the Universe is distributed densely enough, then the combined gravity of it eventually reverses the expansion and makes it collapse on itself. If the average mass density is too small, then the combined gravity of the mass cannot stop the expansion. The boundary density between these two cases is called the critical density, which goes down as the Universe expands.
Until recently, it was assumed that only the force of gravity was important for the ultimate fate of the Universe, and the mass density was too close to the critical density to call, so if the Universe was going to collapse on itself again, then it was not going to be for many, many billions of years.
Recently, astronomers have discovered that there is in fact an additional force that is important for the ultimate fate of the Universe. This force is repulsive and becomes important only when the mass density has become small enough (in an absolute sense), which it did a few thousand million years ago. The expansion of the Universe is therefore not slowing down but rather seems to be accelerating. It seems, then, that the Universe will not collapse on itself at all.
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