On the "tip" in the instructions for Line 32, it says
If you made any nodeductible contributions to a traditional IRA for 2013, you must report them on Form 8606.
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If you make a contribution to a regular IRA (not a Roth IRA) it might be tax deductible depending on your income, and if your employer has a qualified retirement program (like a 401k) or your spouses employer. If you exceed the limits your contributions are reduced or non deductible.
See the IRS website Retirement Topics - IRA Contribution Limits for details.
If you go further down the 1040 instructions, it goes into the IRA Deduction Worksheet (for Line 32). It considers your filing status, AGI, retirement plan coverage, certain above the line deductions, wages and earned income, to determine whether your contributions are deductible. It limits the ability of high earners who have a retirement plan at work to use the IRA deduction.