The PCT enables the U.S. applicant to file one application, an "International Application", in a the U.S. Receiving Office (USPTO) and have that application acknowledged as a regular filing in as many member countries in the PCT in which patent protection is desired. In the same manner, the PCT enables foreign applicants to file a PCT International application in their home patent office, designating the U.S., and have the application acknowledged as a regular U.S. national filing.
The advantage of PCT is that if you file a provisional patent application in the U.S., you can then file within a year in any PCT member country, and have your application enjoy the benefit of the provisional application's filing date. So, even if the invention is publicly disclosed after the provisional filing, no foreign rights are lost with respect to PCT member countries. However, with respect to foreign countries that are not members of PCT, no such priority can be claimed and the application must be filed before any public disclosure.
NOTE: The United States has entered into treaties with some other countries that are not members of the PCT which enable U.S. applicants to file in those countries within one year of U.S. filing.