Many Americans get health insurance as a benefit with their jobs. There are new mandatory coverage requirements for insurance companies that are very expensive: for example, the policies used to cover non-school attending offspring until 18, now it is until 26 years old. They also have to cover maternity, well person checkups, vaccinations, birth control at no cost to consumer, and much more.
Because of the extended coverage, costs are higher.
Some businesses are dropping employee health insurance as a benefit, or using part time workers to avoid the costs.
That is the private insurance. Around half of Americans are covered by government insurance, either Medicare for the elderly and disabled, or Medicaid for the poor. Under the new law, more people will have access to Medicaid, but about half the states, who partially fund Medicaid in partnership with the federal government, have not agreed to the changes.
For people who aren't covered by insurance from work or the government programs are now required to purchase health insurance or pay a fine with their taxes. They can purchase insurance from the federal government, choosing from 4 plans with varying deductibles, etc. The website is faulty, so people are complaining that they can't sign up, a month now after its launch.
Kind of a confusing nutshell.