What is a health insurance exchange?

That is what was established under the ACA or Obamacare in every stat4e. Those states who refused to do that have a federal insurance exchange since it was required by law. You can buy an insurance policy from the exchange and get a subsidy toward the cost of your monthly premiums.

A state run program where a few insurance companies have contracted with them to provide policies that meet the ACA rules. Those programs are then subject to Federal Govt subsidies.

The health insurance exchange is the website that you'd use to purchase health insurance if you qualify for a subsidy.

There are website specifically for a few states but most states use the federal website.

If you qualify for a subsidy signing up through the website is the only way to get the subsidy. If you don't qualify for a subsidy you don't need to use the website ▬ you can get the same plans for the same premium (in most areas) without using the website.