Points are sort of like a special currency. They can be obtained through Donator Packs, Voting, and special events. They can be used to purchase various rewards at the Points Building. The amount of points you have can be seen on the Sidebar, between your Energy and Level.
They can be donated to your Faction, which requires them for some upgrades. The faction can also give points out to members, however points cannot to traded directly between players. The Points Market is a special market just for buying/selling points.