Both of you have some parts wrong, and some right.

Prior to the 2002 BCRA law, for-profit corporations had been banned from electioneering in some states for decades, and that had been upheld by multiple supreme court cases over the years. Other states had no restrictions against corporate electioneering.

BCRA, which Citizens United challenged, had many effects and provisions, among which are: requiring any incorporated entity which is not a political party or 527, but participates in public advocacy for or against any political party, candidate, or ballot issue to register as a "political committee"; required any corporation registering as a political committee to be not-for-profit; barred corporations which are not registered as political committees from any financial contributions to organizations which were registered as political committees; barred any corporation which is not a 527 or registered political committee from making contributions towards any party or campaign; and barred any corporation which is not a 527 or registered political committee from funding or creating advertisements or releasing material which support/oppose any political party, candidate, or ballot issue, within 60 days before an election.

As for the court's decision...

People have a right to free speech under the constitution. Prior to Citizens United v FEC, corporations were not explicitly considered to have all the same rights as people. The constitution makes no mention of corporations. Instead, many past rulings and laws had established the rights of corporations to have and dispose of property with similar protections as private citizens, and other rights were implicitly protected under the 9th amendment's "unenumerated rights" clause.

The assumption implicit in many laws governing corporations, including BCRA, was that corporations existed as legal instruments, not as "associations of citizens".

The ruling had many effects. The most controversial is that it explicitly established that corporations are to be considered as associations of citizens, and therefore all of the protections of the first amendment (and others) apply to them.