Education, Education, Education !! There is no substitute for it.
Briefly, AT BREAK is a non procedural specification of code to be executed when the value of a variable (#FIELD1 in your example) changes.
OLD is a system function which retrieves the last value of the specified variable.
SUM the sum of the specified variable since the last “break”
The statement: ADD SUM(#AMOUNT) TO #TOTAL-AMOUNT is probably an indication that the person who wrote the code originally did not know the difference between SUM and TOTAL. TOTAL is a running sum, which appears to be what is being computed in the code excerpt you posted.
So, you are probably trying to learn Natural, without a class, by reading code, which seems to have been written by someone who is not very familiar with Natural.