A refund offset is when an IRS refund is reduced or intercepted to pay off delinquent debt, such as past-due child support, outstanding student loans, or unpaid state income tax.
You'll get an explanatory letter from the Bureau of the Fiscal Service if your refund is offset. The remainder of your refund will be processed as usual. An offset shouldn't delay it, unless your entire refund was applied to your debt.
More info about refund offsets, including contact info and the appeals process, is available in IRS Tax Topic 203.