The First Contact War

Shortly after discovering that one of Pluto's moons was a mass effect relay encased in layers of ice. Although the discovery of the data archive on Mars had advanced human technology by hundreds of years, the mass relay by mars (know as the Charon Relay) was the final key to unlocking inter galactic exploration. Shortly after its discovery humanity began an aggressive campaign for exploring the galaxy and finding the aliens that left such grand technology. However, this aggressiveness towards exploration and expanding human colonies is what led to the events of the war.

Unbeknownst to humanity, the Citadel Council had made activating certain relays illegal (as to avoid intergalactic incidents or to prevent exploration from getting out of control). Yet a Turian police patrol saw a patrol of ships trying to activate a relay and instead of giving a warning to the patrol or trying to communicate, the Turians attacked and destroyed all but one ship, which made it through the relay before it could be destroyed. That one ship escaped and warned the rest of humanity that life was out there. Retaliation was swift and humanity had met its first alien race in the Milky Way Galaxy. Turians saw their actions as keeping the peace, but humanity saw this event as an act of war; and so began the First Contact War in 2157.

Over the next couple months space fights broke out near mass relays as humanity began its first galactic confrontation. Eventually, a section of the Turain fleet made it to the human colony of Shanxi and began orbital bombardments. The colony surrendered shortly after since it couldn't last long with its forces being destroyed in an instant from above. Humanity quickly regained its forces and took back the colony from Turian control.
These actions quickly got the attention of the Council, which led to peace talks among the two races and humanities introduction into the galactic community.

The results of the war led to humanity showing the Council it could hold  its own and make a difference in the galaxy, and a poor decision within the Turian military to enforce galactic policy. This war also lead to pro- and anti-race groups being created on both sides and throughout the galaxy; some encouraging humanity to work with council or work independently without the Council.