So, in a nutshell, the FTC (a federal administrative agency) promulgated a rule, which has the force of law. That rule was challenged in court in more than one case. (Usually such challenges arise under the Administrative Procedure Act (APA).)

In one case, a federal district court in Texas held the rule invalid and vacated it.

(When a court vacates something, such as a judgment, an order, or a rule, the court renders that thing without effect — and depending on the area of law and the situation, that court action could be retroactive or only prospective in operation. Vacatur is the act of vacating, and the name of the particular legal remedy — it sounds better than vacation, and it should be pronounced "vay-ca-tchure", although some say "VAY-ca-dur".)

The FTC originally appealed that ruling, to defend its own rule. But, with the power shift of the new administration, the FTC has decided to accede to the vacatur (that is, to accept the district court's ruling that vacated the rule, and to dismiss the appeal, thus allowing the district court to effectively wipe the rule off the books instead of the FTC changing the rule itself through notice and comment rule-making).

For more detail about the rule and the procedural history of these cases, and to get a glimpse of the overt politicking happening on the FTC board, check out the links in TFA to the board members' statements — both the Chairman's statement and the dissenting view.

I hope that helps; if anything remains unclear or you have further questions, please ask and I'll do my best to help out.