The VST Programs Standard uses program numbers to allow a plugin to reveal it's presets to your DAW. Using this mechanism, it allows the DAW to load programs into the plugin. This was used for many years, until vendors decided to implement advanced preset browsers with tagging and multiple library support. Unfortunately, Steinberg never updated their VST standard to include support for these features, so currently there's no standard way of retrieving presets from plugins.
A VST program has a program number and a program name. Your DAW does not receive any additional information about the internal structure of the preset apart from the VST parameters set in the plugin.
You can check if your plugin supports VST programs in different applications. Usually, if your plugin has some kind of preset browser which has multiple banks and/or tags, it doesn't support VST programs.