The expansion of the universe was first observed by Edwin Hubble.
The explanation for the expansion of the universe was given by Edwin Hubble by studying the redshifts of different distant galaxies. He also studied Cepheids which explained the relative distances by measuring the brightness of a class of variable stars. It was observed that the graph between redshift and the relative distance was increasing linearly. Redshift was a function of their distances.
It was concluded that in the universe was a single point and as time passed it kept on expanding. This single point is now known as the big bang.