The basic story of the games is that humanity has colonized a planet called Sera because it has a "miracle fuel" called Immulsion, and after we've been there for a while it turns out that a society of creatures called the Locust live underground. They come to the surface and declare war on humans for invading their homeland.
Then it turns out that the Immulsion itself is also a kind of parasitic lifeform that begins infecting the Locust, and in the third game it begins to infect humans, too.
In the third game one of your team members dies to save you and the rest of your team. So the rest of the game becomes a mission to not only save humanity, but to avenge his death.
The game ends with humans pretty much committing double genocide, sending out a huge wave that kills everything on Sera (Locust and Immulsion based lifeforms) but leaves humans alive.
Sooo...we killed both of the indigenous races on a planet we invaded and had no right to in the first place? And we're the heroes?
Then we're treated to a great HOO-AHH! Humans rock! We sure got them back for killing Dom (the aforementioned teammate)!