In a ruling that was feared by Senator's Feingold and McCain, who created the amendment in question, that would fundamentally change the way money influences elections in the United States, the Supreme Court ruled, by a vote of 5-4 that corporations and unions can spend freely on elections. 

The amendment which was found to be unconstitutional was called the Bipartisan Reform Act Of 2002, which prohibited corporations and unions from using their general treasury funds to make independent expenditures for speech that is an "electioneering communication" or for speech that expressly advocates the election or defeat of a candidate.

The case which brought about this ruling was Citizens United v. Federal Elections Committee which dealt with a company that produced a film, painting Hillary Clinton in a negative light during the campaign and was subsequently not allowed to be screened during the primaries because the Elections Commission ruled it violated the Feingold/McCain amendment.

One of the biggest concerns is that individual candidates won't have control over their own message as corporations and to a lesser extent unions, can define the issues and candidates as they please.  They can't give money directly to candidates, but they can create their own front groups and do as they please. 

As an editorial note, this truly is a loss for democracy.

You can read the synopsis of the opinions here.