For the legal eagles out there and the laypersons just curious to take a look at the decision, you can find the Court's opinion here. I'm going to leave the most relevant summary from the opinion below, and for those unfamiliar, note that the "Abood" referenced here is the Supreme Court case Abood v. Detroit Board of Education, which allowed for agency shops in the government context. The Court's view that the ruling in Abood "is inconsistent with standard First Amendment principles" tells you just about everything you need to know about why it was overruled.
I and others will have more analysis of this over the next few hours and days, but suffice it to say that this is a win for supporters of the First Amendement, for government employees, and for taxpayers.
2. The State’s extraction of agency fees from nonconsenting publicsector employees violates the First Amendment. Abood erred in concluding otherwise, and stare decisis cannot support it. Abood is therefore overruled. Pp. 7–47.
(a) Abood’s holding is inconsistent with standard First Amendment principles. Pp. 7–18.
(1) Forcing free and independent individuals to endorse ideas they find objectionable raises serious First Amendment concerns. E.g., West Virginia Bd. of Ed. v. Barnette, 319 U. S. 624, 633. That includes compelling a person to subsidize the speech of other private speakers. E.g., Knox v. Service Employees, 567 U. S. 298, 309. In Knox and Harris v. Quinn, 573 U. S. ___, the Court applied an “exacting” scrutiny standard in judging the constitutionality of agency fees rather than the more traditional strict scrutiny. Even under the more permissive standard, Illinois’ scheme cannot survive. Pp. 7–11.