What does the largest number on the Heroes of the Storm scoreboard indicate?

Solution 1:

It's the number of hero takedowns your team had over the game.

Bottom of the score screen

In this example, my team killed the enemy team 20 times.

Note this won't be a perfect sum of the takedown columns for each team. That's because each hero gets credit for a takedown if they were in the area or did damage to that hero within a short time of that hero's death.