am sure others will have better ways to explain it...
but to me - XX mAH capacity is like comparing it to gallons/liters of fuel your car gas tank can hold - the bigger the gas tank (ie. more gallons/liters it holds) - the more capacity it has and therefore more range you get in your car before you have re-fill the tank. (in this case - a recharge)
I have a couple of the 2900 mAH Panasonic 18650 that would give me a lot longer run time in my lights than a 1400 mAH 18650 cell - am not sure that it would give me double though :shrug:
High refers to capacity, which would be measured in milliamp hours (or possibly watt hours, which factors in the voltage). High drain batteries refer to cells that can handle a higher amp load.