It seems there are lots of good answers already, pointing out the Object INspector, RTTI,
etc. These are all pieces of the puzzle.
If you take away the published keyword, the entire Delphi RAD tool design would require some way to specify which properties are stored in a DFM, inspected in the component property inspector, and can be reloaded at runtime from a DFM when the form or data module is created.
This, in a word, is what Published is for. It is interesting to me that the designers of QT (originally TrollTech, later part of Nokia, later still spun off to Digia) had to emulate this level of RTTI for their C++ RAD library "QT", adding a "published" equivalent and a "property" equivalent, while pure C++ still lacks this fundamental facility.