The verbiage is a bit dense, but here's the upshot: the ACA requires health plans to provide contraceptive coverage to all insured members. Some religious organizations and even a few for-profit companies objected to this requirement, citing religious beliefs.
Jonathan Chait is exactly right about the unspoken conservative position on health-care reform:
Opponents of the law have endlessly invoked “socialism.” Nothing in the Affordable Care Act or any part of President Obama’s challenges the basic dynamics of market capitalism. All sides accept that some of us should continue to enjoy vastly greater comforts and pleasures than others. If you don’t work as hard as Mitt Romney has, or were born less smart, or to worse parents, or enjoyed worse schools, or invested your skills in an industry that collapsed, or suffered any other misfortune, then you will be punished for this. Your television may be low-definition, or you might not be able to heat or cool your home as comfortably as you would like; you may clothe your children in discarded garments from the Salvation Army.