The Rebel Alliance was a loose collaboration of factions and planets opposed to the tyranny of the Galatic Empire.
The scattered groups across the galaxy gradually became more organised and key figures such as Leia Organa, Obi-Wan Kenobi, Luke Skywalker, and Han Solo begin to emerge.
The Emperor tightened his grip however, and was especially interested in trying to turn those ones who were strong in the Force to the Dark Side. His rage against the rebellion knew no bounds and on his orders the peaceful planet of Alderaan was destroyed by the Death Star.
The Alliance eventually prevailed however as much though cunning as force. Stealing the Death Star plans was a huge coup as was getting the X-Wing starfighter which had been in tended for the Empire.
The destruction of both Death Stars and the death of Emperor Palpatine brought about peace and the declaration of the New Republic.