Counter current: the blood flow of the capillaries of the vasa recta is opposite in direction of the flow of filtrate in the loop of Henle. That is, as the filtrate flows towards the medulla through the descending limb, the neighboring capillaries carry plasma towards the cortex and as the filtrate flows towards the cortex in the ascending loop, the capillaries carry the blood towards the medulla.
Counter current exchange: The descending loop of Henle is permeable to water but not ions and the medulla has a higher solute concentration than the cortex. So, as the filtrate descends, water flows out and is absorbed into the capillaries and carried towards the cortex.
The ascending loop o' Henle is permeable to ions but not water (!), so as the filtrate ascends, ions diffuse out and are carried by the neighboring capillaries towards the medulla. Along the ascending loop ions are actively pumped out of the filtrate and also carried towards the medulla, ultimately establishing the osmotic gradient. The gradient that's established through active transport is "multiplied" by the counter current exchange.
The pay off: The immediate pay off is reducing filtrate volume by reclaiming both water and ions from the filtrate into the plasma. The secondary pay off is establishing the concentration gradient so that ADH can control urine concentration by altering the permeability of the collecting ducts which pass through the same gradient.