A deductible IRA can lower your tax bill by allowing you to deduct your contributions on your tax return - you essentially get a refund on the taxes you paid earlier in the year.
You fund a nondeductible IRA with after-tax dollars. You cannot deduct contributions on your tax return.
Obviously, a deductible IRA is a better deal. But whether you qualify for one depends on your income, filing status, whether you have access to an employee-sponsored retirement plan at work and whether you receive Social Security benefits. For more see Who can contribute to a traditional IRA?