Args is the name of the string array brought in by the "main" function. It holds whatever you wrote on the command line when running the program. Something like:
/myprogram 1
would have "1" as args[0]
Integer.pareInt assumes args[0] is a number and casts it appropriately.

When you execute your program with arguments like this:

javac GambleRuin 1 2 3

Then your program will be executed by calling the main function.

The String[] args array will be ["1","2","3"]. Since the arguments always pass as strings, you need to cast them to integers for your program to work, hence parse int

Warning: if the arguments are not integers, then an exception will be thrown and your program will crash.

You could assign value of n as 0 or any other value by default and use if(args.length > 0) { to check whether any arguments is given. Below is full example with comments:

public class Infinity {
    public static void main(String args[]) {

        /*
        Start by assigning your default value to n, here it is 0
        If valid argument is not given, your program runs 
        starting from this value
        */
        int n = 0;

        // If any arguments given, we try to parse it
        if(args.length > 0) {

            try {
                n = Integer.parseInt(args[0]);
            } catch (NumberFormatException e) {
                System.err.println("Argument" + args[0] + " must be an integer.");

                // Program ends
                System.exit(1);
            }

        }

        // All good, n is either default (0) or user entered value
        while(true) {
            System.out.println(n);
            n++;
        }
    }
}

Note: Users which are not so familiar with java, this program can be run by:

1. Saving it to Infinity.java
2. Compiling it with cmd or terminal by writing: javac Infinity.java
3. Executing it with: java Infinity or java Infinity 1000 (or any other value)

Cheers.