A 403(b) retirement plan represents the non-profit counterpart of the for-profit 401(k). The numbers just reflect the section of the U.S. tax code where these plans are defined, and the differences today are highly technical and affect mostly the administrator's reporting requirements. Both plans allow participants to set aside money on a pre-tax basis through payroll deductions. Pre-tax means you reduce your taxable income by the amount you set aside.
You will, of course, pay tax on the money when you "take a distribution," or cash out part or all of your fund, presumably at retirement, or any time after you reach 59 1/2. If you take a distribution before that, you may be liable for a 10% early distribution penalty. However, if you need funds for emergencies like health care expenses, or funds for tuition, buying a home, or if you are disabled, the penalty is waived. The Internal Revenue Service also allows "Substantially Equal Periodic Payments" to avoid the penalty, but be careful: these can run afoul of IRS rules and trigger the penalty.
The major advantage of these plans is that any capital gains in your plan do not get taxed. Unlike other investments, if your funds double, you do not have to pay a tax on the increase when you cash out.
Generally, your employer chooses which firm or firms will manage the organization's account, but you choose how to allocate your investments. You can take a sizable risk, for example, by choosing mutual funds that invest in small companies. Or you can be conservative and buy highly-rated corporate or government bonds. Most likely, you'll want to balance your portfolio with a range of risk.
Many employers offer some percentage of matching funds. If you put aside $100, for example, your employer will contribute up to $100, but usually less. Employer contributions are usually capped at a percentage of your salary. If you earn $100,000 and set aside $15,000, your employer match might be $3,000, or 3%.
Contribution limits are now at $16,500 if you are under 50, and $21,000 if you are over 50. As of 2007, these limits are indexed to inflation, leading to the possibility of them declining in 2010.