We assume that the brightness of all supernovae of Type Ia is more or less the same. We can use them as 'standard candles' to measure the distance to remote galaxies.
The Doppler red shift tells us how fast they were receding from us at the time of the explosion. Plotting these two shows that the expanison of the Universe was slower in the past.
If the expansion of the Universe is picking up, it means it has a non-zero cosmological constant or it contains the repulsive dark energy.
New tentative results may upend this view. The authors of this paper claim that supernovae were fainter when galaxies were younger. The Universe may even reverse its expansion in the future.