Initial value of a variable is the value it has when it initializes, if you have a variable that is Integer and you don't specify initial value it will be null, you can set it to new Integer(0). Variable expression is what the variable "listens to", if you set it to $F{field} and the Calculation Type is Sum, then it will sum the values of $F{field}. Experiment with it, it all depends on the use case.