For those of you asking why this particular law is a big deal, since there appear to be similar state and federal laws, the Indiana law differs from the others in some key areas.
Unlike the federal law, it explicitly states that an individual or business can assert their religious beliefs “as a claim or defense in a judicial or administrative proceeding, regardless of whether the state or any other governmental entity is a party to the proceeding.” To translate the legal jargon: this law directly applies to disputes between individuals, while most of the other versions only concern instances where the government 'forces' someone to act in a certain way.
There are lots of other differences; the Washington Post and LA Times have good articles that explain them well.