Platform screen doors are doors installed on the edge of a station platform, in addition to the doors of any train which cares to stop there itself.
Platform screen doors (PSDs) are usually made of glass or metal, and are usually sliding doors (pocket doors could also be possible, although I can't recollect seeing any). They have several uses;
PSDs are synchronized with the train doors itself. The train driver (or, even more technologically advanced, driverless trains.1) opens and closes the train doors, and, via the wonders of technology, causes the platform screen doors to automatically open in synchronization, although with some margin of delay.
As of writing, PSDs still have some disadvantages:
1. Driverless trains usually have one staff member on them anyway, to operate the doors and for other emergency purposes.
2. Thanks to Damodred for the info.