When you download the Flash Player file it will normally go into your downloads folder.
The file itself will have a .dmg extension which signifies that that it is a disk image.
Double clicking it will create the actual image from which the installation of Flash Player will take place. Just like putting a floppy disk or a CD into the drive.

Once the install has finished, you can safely put that mounted volume into the trash (eject it) and you can also delete the original file that you downloaded, the .dmg file.

FYI: It is important that you do not have these files automatically mounting when your download them. Go to Safari Preferences > General and UNCHECK "Open "Safe" Files after downloading".

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