The premiere of Falling Skies picks up approximately six months after aliens have taken over earth. They've wiped out most of the population.
But there are pockets of resistance fighters in Massachusetts, as the show focuses on the "Second Massachusetts," which is comprised of 200 civilians and 100 army members. The latter group is led by General Weaver, whose second in command is Tom Mason, a history professor at BU.
Tom has three sons: Hal, who helps him fight the aliens; Matt, who is a toddler; and Ben, who has been taken by the enemy. He's one of many kids who appears under some kind of trance when we see him walking with aliens, an odd harness attached to his back.
The Second Massaschusetts is headed out of the city in order to regroup and survive. Tom helps bridge a chasm between Weaver's army and the civilians, who Weaver thinks are holding them back. He does this via a solid relationship with a doctor named Anne. Both Tom and Anne lost their spouses in the initial wave of attacks.