I did a little research and figured this out.
There are two install profiles in core, standard and minimal.
The minimal profile is not shown during installation, because of this setting in the .info file.
If you remove this, you will be given an option to use either the standard or minimal install profile.
If you have a custom install profile, you should create a "profiles" directory in the root folder of your site (outside of core) and put your custom install profile there. If it does not have this "hidden" setting, they you should have the option to use it during the installation process.