What do 3 dots next to a parameter type mean in Java?

It means that zero or more String objects (or a single array of them) may be passed as the argument(s) for that method.

See the "Arbitrary Number of Arguments" section here: http://java.sun.com/docs/books/tutorial/java/javaOO/arguments.html#varargs

In your example, you could call it as any of the following:

myMethod(); // Likely useless, but possible
myMethod("one", "two", "three");
myMethod("solo");
myMethod(new String[]{"a", "b", "c"});

Important Note: The argument(s) passed in this way is always an array - even if there's just one. Make sure you treat it that way in the method body.

Important Note 2: The argument that gets the ... must be the last in the method signature. So, myMethod(int i, String... strings) is okay, but myMethod(String... strings, int i) is not okay.

Thanks to Vash for the clarifications in his comment.

That feature is called varargs, and it's a feature introduced in Java 5. It means that function can receive multiple String arguments:

myMethod("foo", "bar");
myMethod("foo", "bar", "baz");
myMethod(new String[]{"foo", "var", "baz"}); // you can even pass an array

Then, you can use the String var as an array:

public void myMethod(String... strings) {
    for (String whatever : strings) {
        // do what ever you want
    }

    // the code above is equivalent to
    for (int i = 0; i < strings.length; i++) {
        // classical for. In this case you use strings[i]
    }
}

This answer borrows heavily from kiswa's and Lorenzo's... and also from Graphain's comment.