Any money that contributes to a traditional IRA and that you don't deduct on your tax return is a “non-deductible contribution.” You must still declare these contributions on your return, and to do so, you must use Form 8606.Reporting them saves you money in the future. You may not be able to deduct traditional IRA contributions from your taxable income if your income exceeds certain levels. The amount you can save may also be limited, but you can still save for retirement with contributions that you don't deduct. In this case, it often makes sense to make a contribution to a Roth IRA instead of a non-deductible contribution to the IRA.
The availability of the Backdoor Roth IRA usually makes long-term investments in a traditional non-deductible IRA inappropriate. In both cases, contributions are made after tax, but all future growth and withdrawals from a Roth IRA are tax-exempt, while the withdrawal from growth of a traditional non-deductible IRA is subject to taxes as income. In a clandestine Roth, investors make a non-deductible contribution to a traditional IRA and then quickly convert it to a Roth IRA. A traditional non-deductible IRA is obtained when contributions to a traditional IRA (TIra) are not deducted on a taxpayer's tax return.
You may still be able to save on a Roth IRA if you're covered by an employer-sponsored 401 (k) and your income exceeds the limits of a regular IRA deduction. The traditional IRA page explains the basic mechanisms for making non-deductible investments and keeping track of the base, and that page explains the details of using a traditional non-deductible IRA to make a contribution to a clandestine Roth IRA. If your income excludes you from the Roth option, you can simply contribute to a non-deductible IRA and then convert it to a Roth IRA. Non-deductible traditional IRA contributions are the first step in making clandestine Roth IRA contributions and are most commonly used for this strategy.