When you destroy an enemy object that isnt a player, such as DVA's suit or Torbjorn's turret, you will see +### message. What do the numbers mean? Do they actually affect anything? As far as I understand there is no points system.
All the numbers are how much "fire" you get. The blue bar beneath your health is the fire meter, and if it's above a certain threshold then you are "on fire". It drains over time, and every time you see one of those numbers pop up it fills back up that amount.