In school and in practice, yes. I haven't started studying for Reg yet, but it's reasonable to know.
It's one of the ways that the IRS can respond to a court siding with the taxpayer and against the IRS. When the IRS announces a nonacquiescence to an adverse court decision, it's saying that it disagrees with that court's ruling and won't use it as precedence in the future. The effect on precedence is what's important – if you were evaluating a tax position for uncertainty and looking at court cases for precedence, a nonacquiescence means the IRS isn't accepting that case as setting authoritative precedence (especially outside of that specific court's jurisdiction). It doesn't mean that the service won't follow the court's decision in the specific case in question, but if another taxpayer takes the same position as the one that won, the IRS may still reject it and pursue the matter in court.
One common example has to do with methods for allocating expenses when there's rental and personal use of a vacation home. The IRS uses one method, and the tax court allows another. This is a long-standing disagreement, and the IRS refuses to accept the tax court position – the IRS continues to issue nonacquiescences in response to these cases. So the IRS will disallow a portion of a deduction if the tax court method is used and the taxpayer has the option to go to court and get the IRS overruled… but in most cases it isn't worth the costs of going to court.
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