According to a story by Jim Baumbach of Newsday, Derek Jeter and Johnny Damon will swap lineup positions and Jeter will lead off followed by Damon. According to Baumbach, Damon is fine with the decision as the team comes first. Let's look at the switch from a couple of different angles.
First, Jeter has actually played a quarter of his big league games from the lead off position. That's a fairly large sample size. His OPS (slugging plus OBP) from that spot are slightly higher than his career averages (from baseball-reference.com - click on the graphic on the left to see the stats). To be square about things, the Fan is not factoring in the amount of times Jeter batted first in the order by age. If he compiled most of these stats in his prime then that would account for some of the difference.
Damon, on the other hand has a fairly small sample size batting second in the order. He's always been a lead off kind of guy. But that said, Jeter gets on base more than Damon. Jeter also does better leading off the game and leading off an inning. All in all, this seems like a smart move in view of the statistics. Jeter should be on base more often and thus promote more first inning runs.
There are two other things this change in batting position does. First, it gives Jeter slightly more at bats per game (there is not a whole lot of difference from first to second). That should slightly help him on his push for 3000 hits and beyond.
The second thing it does is give the Yankees some flexibility with Damon's playing time. He is pegged as the starting left fielder. But the Fan can see Swisher getting some games out there and maybe even Matsui on occasion. When those times occur, the batting order won't be affected every time as Swisher can be effective in the second spot when he plays. Matsui can stay in his same batting position whether he is a DH or the left fielder.
Nice move, Mr. Girardi.