After-tax contributions are deducted from your paycheck after income taxes have already been paid. That is to say, the contribution is made with tax paid money. The other option is a pre-tax contribution, which reduces your gross taxable income for tax purposes and hence is made with untaxed money.
In either case, the money is allowed to grow tax free in your 401(k) account until distributed in retirement, usually after age 59-1/2. If your account contains after tax contributions, a portion of each distribution is considered a refund of that money. Hence, your distribution is partially tax free. If only pretax contributions have been made, all of the distribution is taxable income. Distributions from a 401(k) plan are fully taxable at ordinary income tax rates. That compares with a Roth 401(k) plan, where all contributions are after tax, but distributions are tax free in retirement.