Basically: Vermont had passed laws in 1997 (signed into law by Governor Dean) restricting both contributions to campaigns (as little as $200 to a state house candidate, up to $400 for a gubernatorial candidate) as well as strict limits on expenditures (how much campaigns could spend), from $2000 for a single-member state representative race up to $300,000 for a gubernatorial campaign.
Previously, under Buckley v Valeo, the Court had found contribution limits constitutional (if they were narrowly tailored), and expenditure limits unconstitutional.
Three justices today -- Breyer, Roberts and Alito -- determined that both sets of limits in this case are too severe, in light of First Amendment and Breyer's traditional pro-democratic process concerns. Breyer writes:
[C]ontribution limits that are too low can also harm the electoral process by preventing challengers from mounting effective campaigns against incumbent officeholders, thereby reducing democratic accountability. Were we to ignore that fact, a statute that seeks to regulate campaign contributions could itself prove an obstacle to the very electoral fairness it seeks to promote.
They uphold the Buckley v Valeo precedent (money = speech, and therefore CFR must be narrowly tailored), but do what can only be described as quasi-legislative analysis in determining that the real-world impact of these restrictions is too much. On the expenditure limits, they reject the invitation to overturn Buckley and deny the premise that "experience . . . has shown that contribution limits (and disclosure requirements) alone cannot effectively deter corruption or its appearance; hence experience has undermined an assumption underlying that case."
The plurality employs five factors in determining that these contribution limits cause more harm to the democratic process than good:
a. The contribution limits appear to significantly restrict the amount of money available to challengers to run competitive elections.
b. The same low limits are imposed on political parties, harming the right to association.
c. The law treats volunteer expenses too harshly, In the context of very low contribution limits, this imposes too high a First Amendment cost.
d. The limits are not adjusted for inflation.
e. The record does not show a particular danger of corruption to justify such stringent limits on constitutional rights.
That's three justices, including the two new members of the Court, agreeing that campaign finance reform is constitutional in general, but just not in the way Vermont attempted it. (Add the three dissenters, and you've got at least six justices stating that this is generally constitutional.)
To get to five votes, then, Justices Scalia and Thomas (no surprise) join them to form a majority, with the separate rationale that Buckley should be overturned and these limits struck down because the First Amendment should not tolerate any restrictions related to political speech. This, they've both said before.
A sixth justice, Justice Kennedy isn't ready to go there yet, but in a brief concurrence he throws up his hands and basically says that while the three-judge-plurality's analysis is correct, these limits aren't seeming like things that the Court is competent to adjudicate, and that every time the Court okays a new campaign finance law, some new legal device (like PACs) comes in to fill the void, so, like, what's the point of trying?
Justice Souter, with Ginsburg and Stevens, would have let the lower courts figure out whether the expenditure limits were working as the most narrowly-tailored option, rather than decide this himself. Believed the contribution limits were both hunky and dory.
Justice Stevens says he's ready to overrule Buckley and declare limits on campaign expenditures to be constitutional.
edited to add: NYU law professor Rick Pildes has some interesting thoughts on what this may portend for the gerrymandering cases.