This program is a graphical sudo for MacOSX.

You give it a command to run and it brings up the system password box.
When an administrator's password is typed in the command is run as root.

A sample running is 
MacSudo -p MyApp rm -rf tempDir

Which would put "On behalf of MyApp, MacSudo requires you to type in your password" into the authentication box that comes up.
Upon a successful authentication, it would run "rm -rf tempDir" as root.

If the -p option isn't given then it will leave out the "On behalf on ___, " and just mention MacSudo.