Eckstein makes every team he plays for better than they were before they had him. He does the little things - moving runners up, making routine play after routine play, etc. - that don't get noticed on a day-to-day basis but translate into 5-10 wins over a 162-game season.
Small case in point, last year's NLCS against the Astros. Houston up 2, Cardinals down to their last out, Eckstein gets on after a great at-bat. Somebody else gets on (Edmonds?) and Pujols unloards with a 3-run homer to win.
He's not a great individual player. He is a great, great team player. In the era of celebrating talented, selfish idiots like TO, that gets overlooked. I doubt there's a manager in MLB - black, while, Asian, Jewish, Mexican. Somalian or Japanese - who wouldn't love to have a guy like Eckstein on his team.
Bill James had an excellent piece on a similar player from the 1980s, Scott Fletcher. Seemingly modest in individual talent, but every single time he was traded the team that obtained him had a significantly better record the following year.
Oddly enough, it was the exact opposite with Bobby Bonds, generally considered a great player. Every team he went to got worse.