The full text is available at
http://www.indystar.com/story/news/politics/2015/03/27/text-indianas-religious-freedom-law/70539772/ and the language is a little painful to parse, but basically, what it does is create a defense against any lawsuit or prosecution that you did/didn't do whatever you're being accused of because of your religious beliefs.
In the face of anyone who raised such a defense, the government would have to show that forcing them to do/not do whatever is claimed to be a violation of their religious beliefs is "(a) in the furtherance of a compelling government interest and (b) the least restrictive means of furthering that compelling government interest."
So, if you consider yourself a good Christian restaurant that is opposed to the evils the "homosexual lifestyle," (say, Cracker Barrel), you could refuse to serve a male couple that came in holding hands and being affectionate on the grounds that having such behavior in your restaurant violated your religious beliefs, even though you would permit a heterosexual couple to engage in the same behavior.
If you were sued/prosecuted for discrimination based on such an exclusion, the plaintiff/government would have to prove that forcing you to serve that homosexual couple was both in the furtherance of a compelling government interest and the least restrictive means of furthering that compelling government interest.
The compelling interest standard is the highest possible standard that the government can be held to, and it's frequently difficult to achieve.