When I switch bikes with someone who does not have a damper, it's obivous what a huge benefit it makes. I vividly remember swapping bikes with someone right before we got onto a long straight road with lots of loose rocks of all sizes. I hated his bike on that stretch, and he bought a damper before his next ride.
It really helps in many types of sections. Sometimes its subtle, sometimes the improvements are dramatic. On rocky, rooted technical uphills - you are way more likely to stay in control and on the line you want. Very important when any mistake means failure. High speed whoops - the bike is way more stable. Where you normally would back down out of fear, you will still be in control.
In the tight stuff, when you get tired and lazy and don't have your weight forward, the front tire is far less likely to wash out or deflect. When you are riding aggressively, you have more margin for error as you can 'save' the bike much more easily.
As you can tell, I am a huge fan of dampers. Best thing since sliced bread.