What do the numbers when destroying non-player things mean?

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.

Just like when eliminating players, the number is the amount added to your On-Fire Meter. It has no gameplay purpose other than letting yourself and everyone else know you're doing particularly well when you reach a certain threshold. See also I'm on fire. So?

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.