Take a balloon and inflate it until it is firm. Then take a soft pen which won't burst the balloon and mark lots of dots all over it, fairly evenly spaced. The balloon is the universe and the dots are the galaxies. Now put an ant on one of the galaxies and begin to inflate the balloon further. From the point of view of the ant, his galaxy is stationary and at the centre, with all the other galaxies moving away and the more distant galaxies moving away fastest of all.
Then put an ant on one of the other galaxies and try to visualise the situation as he sees it. This second ant will also see himself as at the centre of the universe with all the other galaxies rushing away, with the furthest moving away fastest of all. It doesn't matter which dot or galaxy you put the ant on, the picture will always look the same. There is an elastic force in the balloon which is always trying to collapse it, but the expansion resists this force. Its counterpart on a galactic scale is gravity, which is always trying to resist the expansion and gradually slowing it down. Until recently it was thought that eventually gravity would win, and the universe would be brought to a halt and collapse on itself to become a contracting, blue shifted universe, gradually speeding up and hurtling toward destruction in what was called the Big Crunch. But then dark energy threw a spanner in the works.
Dark energy is a mysterious force which astronomers think is speed ing up the expansion too much for gravity to slow it down and halt it. Observations and measurements of the redshift of distant type 1a supernovae are what brought them to this conclusion. However, the measurements are difficult to make and difficult to interpret, so there is always the possibility of error. It also introduces new difficulties, such as a one-off universe with no cause and which will go on expanding forever into the black nothingness of space, making the Big Crunch and the Big Bounce which follows it impossible if current interpretations of the data turn out to be correct. The Big Crunch model has not been entirely abandoned, though dark energy is the favoured theory at present. Dark energy has the disadvantage that no one can explain where it comes from or where it has been hiding, and it also contravenes the 1st Law of Thermodynamics. Some people say that the 1st Law doesn't apply on a cosmic scale, but that sounds like special pleading.
The heat death of the universe, as called2voyage says, is an entropy effect due to the 2nd Law of Thermodynamics, which for some reason can't be abandoned on a cosmic scale, though the 1st Law can. Unlike the 1st Law, the 2nd Law has over a dozen different formulations. From a dark energy, accelerated expansion perspective, it is the cold death of the universe we are talking about, for the black nothingness into which it is reportedly heading is also bitterly cold.