prompt = new Label("Enter integer and press Enter:"); 
sum = 0;

assigns the value 0 to the sum variable.

public boolean action(Event e, Object o)
{
...
}
sum = sum + number; //add number to sum

adds sum (initially 0) to the value of number, assigning the result to sum (destroying its old value).

showStatus(Integer.toString(sum) ); 
input.setText(""); // clear entry field

uses the setText method of the TextField class to set the input text field to the empty string (i.e., the String with no characters in it.

return true; 

specifies that the action method is to return a value of true.

Applet

Label

TextField

Conversion "methods" (I'll explain later what they really are)