Withholding is always based on an estimate of what your taxes due will be. Lump sum payments like bonuses and severance are often subject to excessive withholding because the payroll system may estimate that the larger payment will be typical of other payments you'll receive, which of course it isn't.
With a bonus, you often get this back through the rest of the year. The payroll system sees that you didn't get that bonus again next month and the month after that and withholds less than it usually would. However, this isn't going to be possible with a severance payment. And, of course, your next employer won't know that your previous employer withheld a bit too much.
Your employer will report the lump payment to the IRS the same way it reports all other payments to you. At the end of the year, you will receive a W2 from your employer that includes what they paid you and what they withheld. If the withholding actually turns out to be excessive, the amount withheld will exceed the amount you owe and you will receive a refund.