I'm looking to improve/adjust my wheel alignment on a lowered BMW E36. I have been advised to check the condition of my dampers but I'm not sure how to do that!
With respect to your original question:
What is a damper?
A damper (AKA strut or shock absorber) is "a mechanical device designed to dissipate kinetic energy." In it's automotive use, it works with the springs to absorb the impact of bumps and rough spots in the road before those impacts bother your car and the passengers therein.
In answering a related question, I posted a pretty long answer. Here is the short form of the standard check-your-shocks procedure:
Push down one corner of the car and release.
Watch the motion: the corner of the car should start low, come up and return to rest. Any additional bouncing = bad shocks.
You should also consider the total miles on the shocks. If the shocks only have a few thousand miles on them, there's a good chance that they're fine. If there's 100K miles on them, they're probably done.