They want to eliminate Obamacare entirely and provide money to an HSA to which you could also add your own savings to use to buy insurance on the open market, presumably buying a catastrophic plan and using your HSA to pay out of pocket for most ordinary medical costs. A key to this would be requiring pricing disclosures for basic medical care so people could value shop for care and theoretically put downward pressure on the cost of medical care.
This ignores how much medical costs vary if you pay out of pocket versus what is paid by an insurance plan, for instance, much less the way life or death medical crises distort market forces, but the goal is to make people more educated consumers of their own healthcare to create market pressure on pricing and get the government out of spending so much on healthcare other than Medicare (which I am sure many in the GOP would terminate if they didn’t know that would cause an actual revolution).