The Systems Alliance is responsible for the government and defense of all extra-Solar human colonies, and it represents humanity on the galactic stage. It is a supranational government, with a parliament appointed by sovereign member nations on Earth. The parliament does not convene on Earth, but rather in the Arcturus System on Arcturus Station, the largest human-built space facility. It has direct control over a large spaceborne navy.
The Systems Alliance was chartered by Earth's eighteen most prominent nations in 2148, after the discovery of alien technology on Mars provided access to FTL technology and knowledge of mass relays, ancient point-to-point relays that allowed instantaneous transit between star systems and star clusters. In 2156, the Systems Alliance was given control of the Systems Alliance Military, a force provided by member nations. In the same year, Pluto's moon Charon was revealed to actually be a mass relay encased in ice. After melting it, the Alliance went through the relay and discovered the Arcturus system. They continued exploring outer space using FTL technology and various mass relays, establishing colonies along the way.
Politically, the Systems Alliance had little clout, until the inevitable happened. In 2164 an Alliance exploration force was attacked by an alien patrol while trying to activate a newly discovered mass relay, the beginning of what would be known as the First Contact War. The aliens found the Alliance colony of Shanxi, attacking and occupying it. An Alliance fleet dispatched from Arcturus defeated the enemy fleet and retook Shanxi. The Alliance geared up for full-scale war with the aliens, but war was averted by the alien's peers. The attacking aliens, called turians, were part of a galactic organization known as the Citadel Council, based at an ancient space station called the Citadel. The two other member species, the asari and salarians, noticed the turians preparing for war and stopped them, opening relations with the Systems Alliance. As it turns out, activating dormant relays was restricted by the Council, as in the past hostile species had been found on the other side. Of course, the Systems Alliance could not have known about this. With this misunderstanding resolved, the turians backed off, and the Systems Alliance became the political face of humanity to the rest of the galaxy.
The Systems Alliance grew in power over the next few decades, butting heads with a race called the batarians over control of a region of space called the Skyllian Verge. The batarian government never formally declared war with the Alliance, but they sponsored pirates and slavers to attack Alliance colonies.
In 2183, the Citadel fell under attack by by an AI race called the geth, led by an ancient sentient ship called Sovereign. The Alliance managed to defeat the geth fleet and Sovereign and were rewarded with membership on the Council.
The Systems Alliance has dozens of colonies, spread out among many star clusters. Due to fuel limitations, normal FTL is insufficient to traverse between the star clusters, so mass relays must be used. Not all human colonies are under Alliance control.
The Systems Alliance is a major power in the Mass Effect universe, but its territory is small compared to the United Federation of Planets and tiny compared to the Galactic Empire. Technologically, they are somewhat below the Federation, and far below the Empire. It would possibly be a minor power in Star Trek, although it should be noted they should have been a minor power in the ME universe, too, and the same factors which prevented that may apply in ST. It would be an insignificant power in Star Wars. Their power and influence could be considered comparable to that of the Earth Alliance from Babylon 5.
They possess a fleet of hundreds of ships, ranging from kilometer-long dreadnoughts to hundred-meter-long frigates. Dreadnoughts are rare, and before the Reaper invasion the Alliance possessed at least nine. A starship's main weapon is a magnetic mass accelerator, which accelerates metal slugs to hundreds or even thousands of kilometers per second. A dreadnought's mass accelerator can deliver 38 kilotons of kinetic energy or more with a single shot (roughly 30 TW over time). For defenses, ships use kinetic barrier shielding, ablative armor specialized to stop energy weapons, and GARDIAN point defense lasers. The point defense lasers are noted for having made long-range ship-to-ship missiles obsolete in the Mass Effect universe. Kinetic barriers are effective at blocking projectile attacks, but do nothing to stop directed-energy weapons such as lasers and particle beams.
In addition, they have starfighters, possibly numbering in the tens of thousands (a senior military officer has casually mentioned the option of building 12,000 fighters instead of the Normandy SR-1). Cruisers carry a handful of fighters in the baffles under their armor, while dreadnoughts have hangars; the Alliance also possesses dedicated fighter carriers.
Regarding tactics, dreadnoughts can engage at ranges of tens of thousands of kilometers, while cruisers are limited to thousands, and frigates fight between hundreds of kilometers and "knife fight" ranges of tens of kilometers. GARDIAN defense lasers are limited to within 10 kilometers. At close range, frigates and fighters use disruptor torpedoes, which can bypass kinetic barriers and create fields that warp space-time in a localized area. The rapid asymmetrical mass changes cause the target to rip itself apart.