I imagine you are reacting to the US Supreme Court ruling in Citizens United v. Federal Election Commission, 558 U.S. 310 (2010). This decision (and here I'm summarising a very well-written and footnoted Wikipedia article) held that:
...it was unconstitutional to ban free speech through the limitation of independent communications by corporations, associations, and unions, i.e. that corporations and labor unions may spend their own money to support or oppose political candidates through independent communications like television advertisements.
The article quotes the decision as saying, "If the First Amendment has any force, it prohibits Congress from fining or jailing citizens, or associations of citizens, for simply engaging in political speech."
Note that they mention "associations of citizens" separately from "citizens". They say that "associations of citizens" are protected, separately from the rights of individuals who make up the association. This is not all that different from treating a Corporation as a separate legal entity from the persons who own the corporation, or who work for the corporation.
There is a related concept of Corporate Personhood, which also has a well-written Wikipedia article. It summarises the concept as:
Corporate personhood is the legal concept that a corporation may sue and be sued in court in the same way as natural persons or unincorporated associations of persons. This doctrine in turn forms the basis for legal recognition that corporations, as groups of people, may hold and exercise certain rights under the common law and the U.S. Constitution. The doctrine does not hold that corporations are "people" in the most common usage of the word, nor does it grant to corporations all of the rights of citizens....
This article says, in talking about political-spending aspects of Corporate Personhood, "It should be noted, however, that neither [the Citizen United nor a "Buckley" (1976)] decision relied on the concept of corporate personhood."
I think it's worth also mentioning, related to protections corporations have under the First Amendment, some misunderstandings about the Citizens United decision from that Wikipedia article:
This ruling was frequently interpreted as permitting corporations and unions to donate to political campaigns, or else removing limits on how much a donor can contribute to a campaign. However, these claims are incorrect, as the ruling did not affect the 1907 Tillman Act's ban on corporate campaign donations (as the Court noted explicitly in its decision), nor the prohibition on foreign corporate donations to American campaigns, nor did it concern campaign contribution limits. The Citizens United decision did not disturb prohibitions on corporate contributions to candidates, and it did not address whether the government could regulate contributions to groups that make independent expenditures. The Citizens United ruling did however remove the previous ban on corporations and organizations using their treasury funds for direct advocacy. These groups were freed to expressly endorse or call to vote for or against specific candidates, actions that were previously prohibited....
If you are interested in this subject, I highly recommend reading the Wikipedia articles on both Citizens United and Corporate Personhood, and following the links they contain. Good work, Wikipedians!