Corporation - a company or group of people authorized to act as a single entity (legally a person) and recognized as such in law.
i.e. It's a way for more than one person to own a business.
I'm often surprised at the number of people that will spout off about topics when the don't even know the definitions of the words they're using. If you own a family business and want to share ownership, it has to be a corporation. If it isn't, it will be under the ownership of one family member and there will be a legal and tax nightmare when that person dies.
They did not ask to be put into the situation where they control the womans healthcare. The government forced them, by law, to provide health care. Then the government forced them, by law, to include contraceptive devices that abort a fertilized fetus. (many of the contraceptive devices covered kill the post-fertilized egg) Their only option out was to pay a fine that would go directly to paying for the very same services they oppose.
From their point of view the government just required them to pay for their employees to have the ability to murder babies. Now, you can disagree with that point of view, I know I do. But it really is their point of view. They really do view it has killing babies. That's a violation of their ability to freely express their religion. The government could have addressed this a dozen different ways. Exempting them from the penalties if they didn't provide the care would have been the simplest. But they didn't. The whitehouse should have seen this coming, they should have provided a religious exemption, but they didn't.