It's important for getting loans (mortgage, car loan, etc.) and for credit cards. The better your credit, the less you'll pay for a loan. Of course, if you have no intention of settling in the states permanently you don't need to worry about that.
However, as you have better credit, you'll be eligible for better credit cards, which will give you better rewards, points/miles, that sort of thing. There is a whole subculture of people who get lots of these points/miles, and for a graduate student it can be a nice perk (i.e. not having to pay for travel).
First things first - when you get to the USA, open a check account (make sure it's no-fee) and a savings account (if you can, especially if you get your funding in a large sum and don't need it all right away). Then, ask the bank about bank credit cards (again, try to get a no-fee card) so you can start building your credit history.
http://en.wikipedia.org/wiki/Credit_score_in_the_United_States