Skillshots are kills you achieve in cool or stylish ways. There are a total of 135 skillshots in the game. The more unique way you kill your enemy, the more skillpoints you will receive, which means you'll be able to upgrade your weapons to hold more ammo, unlock special secondary charged shots for each gun, and even replenish your ammo supply should you run dry. Every time you first perform a skillshot, you get five times the points you normally get; i.e. you perform the Graffiti skillshot for the first time (normally worth 25 points) and you get 125 points. As you progress through the story and purchase charged shots for your guns, you will unlock access to more and more skillshots.
As mentioned already, you get 5 times the normal amount when you first perform a skillshot. Also, if you kill multiple enemies with the same skillshot, then you will have your score multiplied by how many you killed. If you killed 3 enemies with the Environ-Mental skillshot, then you'd get 50SP x 3 for a total of 150 points.