Resistance told the story of Nathan Hale, a solider that fought in the military against the invading Chimera. The military forces of the world came together to hold back the Chimeran invasion. That didn't go so well. Resistance 2 takes the battle to the United States, where Hale helps fight off a full-scale invasion on both of the country's coasts. That didn't go very well, either.
Resistance 3 is very different from those game. The story has progressed to the point where the war has been lost, and now the world has been taken over by the Chimera. The invasion is fully underway, and the surviving people of the world are still adjusting. Joseph Capelli is the main character; and those who played Resistance 2 will know him very well. How he relates to Nathan Hale is a huge spoiler for those that didn't finish Resistance 2.