As mentioned in the description of the Climbing skill, "falling is easy; it's the landing that hurts." Breakfall can help to make those landings somewhat less painful.
The biggest benefit of Breakfall is that a character can fall further without taking damage. The distance that a character can safely fall (as determined by the GM based on the landing surface) is increased by a percentage equal to their Breakfall skill level.
Rutger failed his Climbing check (see the Climbing skill description) at an altitude of 50m above the water. His skill level in Breakfall is 62. Since the safe distance for falling into water is 30m, he can fall 48.6(=30+30*.62=30+18.6) metres without taking damage. Since he fell 50m, he took damage for only 1.4(=50-48.6) metres, a total of 4(=1.4*3 rounded down) points, instead of 20m which would have caused 60 points of damage.
Another bonus of having the Breakfall skill is that the player chooses where the damage will be taken, rather than having it assigned by the GM. The only restrictions on this are that at least two hit locations must share the damage (assuming at least two points of damage is inflicted), and no damage can be assigned to the head.
When Rutger fell, he was already sorely wounded. Therefore, when he hit the water, he decided his relatively uninjured legs should take the falling damage. He took three points of damage on his undamaged left leg, and the remaining point on his slightly wounded right leg.
The final benefit is that a character with Breakfall skill can get up immediately after hitting the ground, instead of losing a round as unskilled characters do. This is especially handy in combat situations, when a character has lost his footing or been knocked down by an opponent.