Imagine horns as a sign of aggression; to 'draw/pull your horns in' is to act less confrontational. He was quite bold in the meeting, but he'll have to pull his horns in now.
Pro Tip 2/3
Conflict De-escalation
Use it when someone needs to reduce tensions or stop being combative. The debate was getting heated, so I pulled my horns in to keep the peace.
Pro Tip 3/3
Less Ambition
It can mean to curb your ambitions if they're seen as unrealistic or causing issues. After the loss, the coach said we had to draw our horns in and focus on simple wins.