To privatize is to switch ownership or control from public, or government-run, to private. The US has a history of deciding to privatize previously government-controlled railroads.
If profit making companies took over every school in the country, turning all public schools into private ones, it would privatize education. Most countries have a variety of public and private industries — in the US, the post office, many schools, public universities, and the police, among other services, are in the public sector. If this changed, they would privatize.