The Alliance to Restore the Republic, commonly known as the Rebel Alliance,Alliance, or the Rebellion, was a resistance movement formed by Bail Organaand Mon Mothma to oppose the reign of the Galactic Empire. Before the Alliance came to be, another less organized movement to oppose the Empire existed, which was secretly led by Organa. This early group came together from a series of rebel cells, including the crew of the Ghost and the Phoenix rebel cell.
The Alliance was born from the remnants of the Jedi Order and with the support ofrenegade members of the Imperial Senate such as Bail Organa and, later, his daughter Leia. Founded and united by Organa, the early rebels were assisted by several surviving Jedi, such as Ahsoka Tano, Kanan Jarrus, his Padawan, Ezra Bridger and later Luke Skywalker. Clone officers such as Captain Rex also assisted in the initial movement.
As opposed to waging all-out war, the Alliance waged a war of attrition against the government, establishing small settlements across the galaxy instead of totally controlling a planet.
When the Alliance successfully stole the plans for the Empire's ultimate weapon, the Death Star, and destroyed the space station in the Battle of Yavin, the tide of the war began to change and the Rebel threat begun to prove a severe thorn in the Empire's side. However, under the command of Darth Vader, the Imperial forces succeeded in defeating the Alliance on Hoth, driving their remaining troops back into hiding.
Eventually, the Alliance prevailed against the Empire and badly crippled it when they launched an attack against the second Death Star during its construction. Not only did the Rebellion manage to destroy the space station, but their Jedi Luke Skywalker also managed to redeem his father Darth Vader who killed the Emperor Sheev Palpatine before dying himself in the Battle of Endor. The Rebel Alliance was soon reformed into a fledging New Republic.
By the time of the Battle of Yavin, the Rebel Alliance had chosen a red starbird as its symbol and logo.
(source Star Wars wiki)