Basically, your tax refund gets offset (garnished/levied/taken) by a government entity authorized to do so. In the case above, she had an unpaid traffic fine which had escalated to the point that the state of Utah took part of her tax refund. Here in Utah, the state can offset state tax refunds to pay for various things (like judgments). See 59-10-529. Overpayment of tax — Credits — Refunds.
A federal offset looks a little different, but it’s really the same concept.
As to how this relates to bankruptcy, well sometimes you have to show this letter to the bankruptcy trustee to show that you never received your refund. So don’t lose the letter.
Unfortunately, once the money is gone, it’s gone. You cannot file bankruptcy and hope to get the offset funds back. On a positive note: at least the offset refund went to a debt she would have had to eventually pay back.