The main difference between the two types of IRAs is when you pay taxes on your investments. Traditional IRAs can delay the taxes until retirement, but with Roth IRAs, you pay tax now rather than later.
Here's how it works: With a Roth IRA, there is no up-front tax break, but you don't have to pay tax on withdrawals in retirement. That's the opposite of a traditional IRA, which may allow you to deduct at least part of your contributions if you qualify, but requires you to pay income tax on money you withdraw in retirement. Both accounts allow investments within them to grow without getting clipped by taxes each year.
There are other differences too.
Roth IRAs offer a bit more flexibility than traditional IRAs do. You may withdraw your contributions to a Roth IRA penalty-free at any time for any reason (but you'll be penalized for withdrawing any investment earnings before age 59 ½ unless it's for a qualifying reason). If you converted money from a traditional IRA into a Roth IRA, you can't take it out penalty-free until at least five years after the conversion.
Roth IRAs also let you leave your money untouched for as long as you like. With a traditional IRA, you must start making withdrawals called "required minimum distributions" after you reach age 70 ½. And while you can no longer make contributions to a traditional IRA after you have turned 70 ½, you can keep contributing to a Roth IRA regardless of your age.