Why do you get out of breath more easily when you climb a mountain?

The air is thinner, there is less oxygen molecules per volume of air (the air is less dense) therefore to absorb the same amount of O2 into your blood at 4000ft as at 0ft altitude you have to breath more/ more deeply.

Also, you're climbing a mountain (going uphill) which uses more energy than going flat as you have to work against gravity.