"IRA" stands for "individual retirement account." A traditional IRA is a retirement account that's opened and managed by an individual (that's you).
Individuals are allowed to contribute up to $5,500 in a traditional IRA (as of the year 2013). The money you contribute is given similar tax treatment to money that you put in a 401k retirement plan: both are "tax-deferred." That means that you don't pay income taxes on the amount you put in. If you earn $80,000 and you contribute $4,000 to a Traditional IRA, for instance, you'll be taxed as if you made $76,000. (For the sake of simplifying the example, I'm excluding other deductions).
You can open a Traditional IRA at any brokerage house like Schwab, Fidelity, TIAA-CREF or Vanguard.
Traditional IRA's typically get less attention that their more-famous counterpart, the Roth IRA.
Also Known As: Trad IRA
Examples: Sally earns $120,000 per year. She contributes $17,500 to her company 401k plan and another $5,500 to a Traditional IRA. Assuming she has no other deductions, she's taxed as though she only earned $97,000. (Sally will most likely claim other deductions, but that's besides the point).