A nondeductible contribution to a traditional IRA occurs when income higher than a certain amount limits the taxpayer's deductible contribution. Any contribution above the allowed deductible amount is considered "after tax" money and tracked on Form 8606. It is not taxed again when funds are withdrawn from the IRA.
For 2014, the general limit for IRA contributions was $5,500, with an additional $1,000 for taxpayers age 50 and older, or the taxpayer's taxable compensation, whichever is less. Contributions up to the general limit are fully tax deductible unless the taxpayer's adjusted gross income is above an annually adjusted threshold. The threshold is lower if the taxpayer or spouse participates in a retirement plan. IRS Publication 590 shows the annual limits.