You can picture this as a balloon with little dots. The balloon is the universe and the dots are the galaxies. When the balloon is blown up bit by bit, the universe is growing and the galaxies are moving away from each other.
People think that the universe started as a result of a gigantic explosion, the big bang, which started the current expansion of the universe.
A millionth second after the big bang there was a temperature higher than 10 billion degrees Celcius (!). The universe was filled with energy in the form of photons (little packages of radiation or radiation parts). Under some circumstances photons can change into matter. This happened at the birth of the universe. After that, most of the photons changed back to radiation, but the remaining part formed the atomic parts that form the universe as it is now. When the universe was 10 seconds old, all the protons, neutrons and electrons had already been formed.
Immediately the universe started to expand and cool down. After 3 minutes the temperature was "only" 1 billion degrees Celsius. There was a chemical reaction between the protons and the neutrons. After the reaction kernels of atoms developed, like helium.
After a couple of thousands of years the temperature had decreased to about 3000 degrees Celsius. The effect was that the protons and the electrons melted into hydrogen atoms and the helium kernels became helium atoms. Furthermore the universe became transparent because it was still expanding.
These days the radiation in the universe is giving a temperature of about 270 degrees Celsius or 3 Kelvin. That is only 3 degrees above the absolute zero.
Most astronomers think that the universe will go on expanding. They speak about an open universe. There are also
astronomers that think that there is enough matter to stop the expansion of the universe.
They speak about a closed universe. The universe will collapse and will end in a big
"shrink". After that there could be a new big bang and the story will start all over again from the
beginning.