Previous interface
The options at Edit Program > Information > Publish previously looked like this.

The difference between Publish, Draft, and Remove from public listings was not clear.
New interface
The options at Edit Program > Information > Publish now look like this.

Publish Status
Options are Draft or Published.

When a program is in Draft mode, it will not appear in public listings, and the program's link (the permalink or URL) will be invalid.
The program will not appear in the list of program pages, will not be displayed via the website integration plugins (like WordPress), and will not appear in the Marketplace.
Publish to
These options only have an effect when the program Publish Status is set to Published.
If the program Publish Status is set to Draft, these options will not have any effect even if they are checked.

Publish to Program Pages, Plugins
When the program status is Published, and the Publish to Program Pages, Plugins box is checked, this program will appear in the list of program pages. It will also be displayed via the website integration plugins (like WordPress).
When the program status is Published, and the Publish to Program Pages, Plugins box is unchecked, this program will not appear in the list of program pages. However, if you provide the program's link (the permalink or URL) to a guest via email or another means, they will be able to follow the link to view the program description page.
Marketplace
When the program status is Published, and the Marketplace box is checked, this program will appear in the Marketplace. This applies only to centers that have already configured their software to list programs on the Marketplace.