The semi-colon is there in case you include this script just after some 'bad' script that doesn't properly close off its last line with a semi-colon. In this case it's possible the two scripts would be combined and result in invalid code. For example if you are merging multiple script into a single response.

The () at the end is executing the function. This is creating a closure. Private variables and methods can be declared within the scope of this function that cannot be accessed from outside the script.