I’m completely Mass Effect ignorant. Care to elaborate?
There's a lot of lore there, so a Mass Effect wiki might serve you better, but to elaborate on the specific topics I mentioned:
Mass Effect gets its title from the effect generated by a rare element known as Element Zero (colloquially, Eezo), only generated during extremely high-energetic events such as supernovas. When exposed to different electrical charges, Element Zero can be manipulated to generate fields within which mass and local gravity are altered. It's used to generate gravity on starships, increase the mass of projectiles in weapons (so a handgun can fire tiny projectiles that still hit with the force of a regular-sized bullet), and to enable FTL travel by reducing an entire starship to negative values of mass.
Occasionally, as a result of deliberate or accidental exposure during pregnancy, children are born with traces of Element Zero in their brains. Those who don't suffer horrible birth defects can go on to develop the ability to manipulate mass fields through mental effort. The amount of Eezo in their brains only allows for tiny manipulations, like pushing a penny across a table, but several races have developed Biotic Amplifiers which link to the wearer's brain and provide additional power and Eezo for them to manipulate, allowing them to generate mass fields large enough to manipulate much larger objects. It's pretty much equivalent to the telekinetic aspects of the Force in Star Wars.
The hive-mind race I mentioned is the Rachni. They did the whole "swarming invasion" thing a few thousand years ago, in what was known as the Rachni Wars. However, during the first game the protagonist can encounter a Rachni Queen and discover that the invasion was a misunderstanding - elements of the Rachni had become cut off from their original hive mind, and had reverted to a feral nature, acting on instinct. The actual hive mind is more sympathetic, and would not have intentionally hurt anyone without provocation.
The Salarians are a short-lived species, with an average lifespan of less than forty years. They have an analytical mindset, and their short lifespan has led to them thinking and acting very quickly. It can be hard to keep up with a Salarian in conversation, as they tend to swiftly move from observation to conclusion before flitting on to some new avenue of thought. Culturally, they tend towards research and espionage, preferring to think their way out of a situation rather than applying direct force.
The Krogans are native to an incredibly hostile and inhospitable world, Tuchanka. Their biological adaptation to that environment was to breed in droves, hatching large litters of offspring, most of whom would not reach adulthood. During the Rachni Wars the Salarians uplifted the Krogans technologically, turning them into shock troops to use against the Rachni. However, once the war was over, the Salarians realised they had a problem: The Krogans, no longer confined to their homeworld with its incredibly harsh environment, would quickly outbreed every other major species and become a plague to dwarf that of the Rachni. So, they secretly engineered a plague and administered it to the Krogans - the genophage, specifically designed not to completely sterilise them, but to reduce their successful birth rate down to match the survival rate their species used to have prior to becoming a technological society. Krogans are, naturally, rather pissed off with the galaxy in general and Salarians in particular, but they so far haven't gone to war with them.
Elcor are large quadrupeds similar to gorillas in size and stance. Their natural form of communication includes a combination of speech and other more subtle indicators such as pheromones that don't translate well when speaking to other species, so that they can't realy express emotion through vocal inflection. They've overcome this by prefacing each sentence with a statement of the emotion it's meant to convey, e.g. "Reproachfully: Please refrain from pointing that firearm at me."
The Hanar are an aquatic species that look like a combination between squid and jellyfish. Graceful and agile in water, they're a lot less capable outside it, relying upon mass-effect fields to let them 'float' upright. They're religious zealots, worshiping a precursor race called the Protheans, who they refer to as the Enkindlers.
The Reapers are the big-bads of the setting - massive biomechanical intelligences, each one having the size and capabilities of a massive spaceship, who generally reside in the 'dark space' between the galaxies. They are extremely ancient in origin, and have locked the galaxy into a cycle of destruction and rebirth in order to serve their own needs. Roughly once every 50,000 years, they invade the galaxy and consume all sentient life in order to reproduce - an entire planet's population may be broken down and used to form the genetic 'core' around which a new Reaper will be grown. They systematically exterminate all life forms in the galaxy that have grown to sufficient sentience to create any kind of technological society, and then, wiping the slate clean, they leave behind the mass relays and other technological assets that will allow new species to arise to form insterstellar civilisations, and retreat to intergalactic space, there to wait out the evolution of new sentient species in the galaxy, until once again those species develop to the point of being ripe for a new reaping.
The Protheans were the dominant species in the galaxy at the time of the last Reaping, and they managed to leave caches of information behind in order to clue-in the galaxy's current occupants as to the fate that awaits them. The Mass Effect trilogy revolves around the discovery of that information just barely in time to actually do something with it, and the subsequent attempts to prepare for and fight the invasion.
