Such a wonderful legal expression: "accede to vacatur". In all matters of jargon it pays to be wary of "false friends" but the layman's reading of words close to this wouldn't be a million miles off the meaning.

Perhaps Congress could pass something most people want?

Could someone translate it to English please?

I'll offer a broad summary of the procedural meaning, but not of the substance of the rule.

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.

FTC is vacating the non-compete ban.

This is inaccurate; see my other comment.

End result is the same either way whether FTC allows it to happen through inaction, or changes it themselves. Point being, labor fucked once more, and capital gets what they want.

This might appear to be the case to a layperson but it is in fact more nuanced.

Scratching the surface:

Democratically, the public enjoys participation in policy development through notice and comment rule-making, but not through this accession/acquiescence (which is politically motivated).

And legally, the public can (or can more-easily) challenge and seek invalidation of rule-making, but cannot (or cannot as easily) challenge effective policy choices made through litigation strategy in cases in which the agency is adverse to a single party, to the exclusion of non-parties and the public generally.

Of course it goes much deeper than this and there are many other differences and considerations.

In this instance, your view of the capital/labor outcomes is probably roughly true, and I agree in principle; but the same procedure could happen with opposite effects in a different administration and with contrary rules, for example.