In the top of the ninth, the score was tied 0-0. The 7-8-9 hitters were due up--Jerry Hairston, the pitcher in the 8 hole, and
Brian Bixler Alex Cora, the position player unconventionally hitting ninth.
Hairston popped out, and then pinch-hitter Matt Stairs and
Bixler Cora got base hits. If the Nationals were using their most common line-up, it would have been Roger Bernadina (.308 OBP) and Ian Desmond (.271 OBP) due up. The Nationals best hitters--Jayson Werth, Danny Espinosa, Laynce Nix, Mike Morse (oy, is that an ugly list of "best hitters, but I digress)--probably would not have gotten a chance to hit in the inning at all.
But since Werth was hitting first, he came up and drew a key walk, loading the bases and advancing the lead runner to third. Espinosa, hitting second, drove in the go-ahead and eventual winning run with a sac fly, and Nix, hitting third, drove in another run with a base-hit. Drew Storen was able to close it out in the ninth, and the Nationals went home winners.
Sure, it's possible that the Nationals still would have scored in the ninth with a traditional lineup--putting a fast guy who isn't among your top 3 hitters in the lead-off spot, followed by maybe the 5th or 6th best hitter in the 2nd spot. But it's less likely. And it's possible that they still might have scored in the tenth inning, but then that would have forced the relievers to get three more outs.
The point is that by putting your best hitters at the top, they get more chances to hit, and you increase your odds of scoring and winning (by an infinitesimal margin in any given game, but still). Pretty much every softball team playing on the National Mall gets it, and it's nice for once to see a major league manager get it too--and get rewarded.