What's the difference between local and external parameters?

You don't necessarily -need- the extra label names, but they can clear up confusion. And they don't have to be identical.

Compare these two functions.

func appendString(myString: String, withString s2: String) {
  return myString + s2
}

appendString("Hello", withString: "World")

func appendString(s1: String, s2: String) {
  return s1 + s2
}

appendString("Hello", "World")

In the first function, it's a lot more clear that the first parameter is the string I want to add on to, and that the second parameter is the thing I want to attach to the end of my primary string. In the second string--how do you know, exactly, that s2 will be added onto the end of s1? You can look at the implementation, or you might be able to reason that it's just common sense, but there's no guarantee it will be.

Or take a far more likely (and more ripe for confusion) example. Somewhere in the code, someone calls this function:

registerEmployee("Adam", "Nathaniel")

Which parameter is the employee's first name? All depending on the country and personal preferences, a name might be filed as Family Name, First Name or First Name Family Name. If the function were defined like this:

func registerEmployee(#lastName: String, #firstName: String) {
///do stuff
}

registerEmployee(lastName: "Adam", firstName: "Nathaniel")

It becomes clearer, right?