On OS X, "Administrator" is not the same thing as "root." Administrators are on the list of sudoers, meaning they have permission to act as root if they so choose.
On the command line, one can run commands as root by using the sudo (Substitute User DO) command first, and then authenticating with their password, but regular users are not allowed to do this. When OS X asks for administrator privileges, it is likely because it needs to do something as root, so you need to enter your password even if you are logged in as an administrator.
It is possible to enable the root account for regular login, which would circumvent the need to reauthenticate; however this is not recommended as it makes it far too easy for you "or someone else with physical access" to mess with/up your system.
And in case this is not clear: root is user id 0, and operates above filesystem permissions and the like—it's basically god mode for *NIX systems.