Your employer will take from your pay the amount that you designate to be your elective deferrals and will deposit the money into your traditional 403(b) account. There your investments will grow tax deferred. While still working for this employer you won't be able to take this money out of the 403(b) until you reach age 59½ except possibly for hardship. Distributions from the 403(b) will be subject to income tax and, if you have no exception that applies such as being age 59½ or over, to a 10% early-distribution penalty. At age 70½ (perhaps age 72 if certain legislation now in Congress becomes law) you will be required to begin receiving distributions.
Your taxable income is reduced by your employer will reducing the amount in box 1 of your W-2 by the amount deferred and including with code E in box 12 of your W-2 the amount deferred. Depending on your circumstances, your elective deferrals might also qualify you for a Retirement Savings Contributions Credit (a tax credit) of as much as 50% of the first $2,000 deferred.