When you print a PDF (or any other format) from an application, several sub systems are involved. The application (such as Adobe Reader) makes calls to the graphics subsystem of the OS (such as GDI on Windows). The OS, in turn passes these calls to the printer driver which is responsible for converting these calls (such as draw line, fill path, etc.) to instructions that are understood by the printer that you selected. These instructions are referred to as the page description language or PDL. Examples of PDLs are PostScript and PCL. This abstraction is good because applications no longer need to ship their own printer drivers. The downside is that the API of the graphics subsystem and the PDL both put restrictions on the richness of your graphics.
Transparency is a typical feature that is present in PDF but only limited available in PostScript. To achieve the same visual result, the feature is approximated. In case of transparency this is called flattening as Max Wyss points out.
By the way, applications (such as Adobe Acrobat) may choose to by-pass the OS and driver and generate the PDL themselves. This is referred to as pass-through printing. Although this circumvents the limitations of the graphics subsystem, the output is still bound to the PDL of your printer.