Java built-in functions" is a reference to the collection of java classes you have in your JRE. There is the Math class for example, which lets you perform various mathematical operations like cosine, sine, square roots, etc. There is also the String class that lets you manipulate strings, the File class, Scanner class, Graphics class, etc. All of the functions located inside of those classes (among thousands of other ones) are built-in functions
examples:
Math.min()
String.replace()
Scanner.nextLine()
Applet.newAudioClip()
Object.toString()
Integer.parseInt()
Double.parseDouble()
DecimalFormat.format()
Also some of your confusion might stem from the fact that java programmers tend to use the word "method" instead of "function", but they are both the same thing.