The Battle of Badr is fought between Muhammad's Muslim followers from Medina and the Quraish tribe of Mecca. This is a very important battle in the early history of Islam and one of the few battles specifically described in the Qur'an. The decisive victory of Muhammad is treated by Muslims as a sign of God's favor and of further Muslim military victories in the future.
Although the Quraishi army should be a powerful opponent, they are apparently undermanned, unorganized, and unprepared. In the Qur'an, though, the Muslims are helped by waves of angels who descend to frighten the Meccans — and this is treated by Muslims as literal, factual history.
In traditional Arab society victory in battle is incredibly important. So the victory here makes Muhammad a respected leader in the Arabian peninsula, giving him the prestige and power necessary to advance his religious cause significantly. Victory at the Battle of Badr establishes both the authority of Muhammad and the authority of Islam for centuries to come.