Path dependence refers to how past choices structure the present, making some decisions impossible, others more costly and some less costly. The most obvious example these days is extinction--if an animal becomes extinct, then most options about that species become moot, unless the fantasies of Jurassic Park become reality.
My favorite example is in Back to the Future. At a key point, Dr. Brown (Christopher Lloyd) informs Marty McFly (Michael J. Fox) that they cannot change things at that moment, as the timeline has already split off. The only way to change things would be to go back in time to change the initial event back to the original way it took place. In reality, we don't have time machines, so we are always stuck with the effects of past decisions.
Today's example is the Presidential Salute. As an op-ed in today's NYT documents, Presidents saluting violates the normal requirements--uniforms, wearing a hat, etc. Reagan started this, and every subsequent President has been compelled to follow suit or be seen as a poor commander-in-chief or unpatriotic. If Reagan had not saluted anyone, then Bush would not have felt compelled, then Clinton would not have had forced to display a poor command of military etiquette (and underlined his status as a draft dodger), then Bush jr. would not have been displaying the one thing he learned while in the Reserves during the Vietnam war, and then Obama would not have been compelled to display a pretty tidy salute this week when bodies were coming back from Afghanistan.
Of course, the bigger and badder forms of path dependence are Obama starting his presidency with two wars to figure out, failing banks, failing car companies, a health insurance crisis and empowered health insurance companies. He didn't choose the cards he was dealt, and he cannot play his hand anyway he wants. Still, leadership means taking the given situation and pushing as much as you can to do the best with it, including challenging precedents and creating new patterns that become institutionalized.