For most students, you can see the importance of claiming extra allowances on your W4 forms during your summer internship now. For my summer internship, even though I tried to claim as many allowances as I could, my average federal tax rate was at 10%. That is double what I should have been paying out! My total loss from not claiming enough allowances to get a more accurate amount of tax withheld would be the extra amount that was withheld times whatever I could have expected to earn on that money over the time period until I get the refund. Usually as a conservative measure, I would use the interest rate on my savings account as what I would have earned, and in this low interest environment, it means it isn't much of a loss. In times of higher interest, it is more important to make sure you claim lots of allowances as a summer intern to not get too much tax withheld. Another circumstance is when you need cash early to make certain purchases. You don't want to have to wait until next April to get your money back from the government.
Especially if you file your own taxes year after year, it is important to keep an eye on your effective tax rate and how it changes over time. You should try to pinpoint what changes each year that changes your effective tax rate: maybe you earned higher income which pushed you into a higher tax bracket or you had a tax credit last year that expired this year. And if your effective tax rate keeps rising year after year, don't be too sad about it. The most likely reason is that you are earning more money.