Platform dependent typically refers to applications that run under only one operating system in one series of computers (one operating environment); for example, Windows running on x86 hardware or Solaris running on SPARC hardware. Sometimes, it means the same as "hardware dependent" or "machine dependent" and refers to applications that run in only one hardware series with the operating system not being relevant.
In contrast, "platform independent" means that the application can run in different operating environments. Applications written in Java are a prime example. See platform