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I assume that the second formula actually looks like this:
=SUM(OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0),1)
where ID is the name of the column.
Let's say that the header of the column is in A2. A1 should either contain text or be empty.
In A3, Table1[[#Headers],[ID]]:Table1[@ID] is equivalent to A2:A3.
OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0) is A1:A2.
SUM(OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0)) is SUM(A1:A2) = 0 because A1 and A2 don't contain numbers.
The entire formula returns 0 + 1 = 1.
In A4, OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0) i equivalent to A2:A4.
OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0) is A1:A3.
SUM(OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0)) is SUM(A1:A3) = 1 because A1 and A2 don't contain numbers and A3 = 1.
The entire formula returns 1 + 1 = 2.
In A5, OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0) i equivalent to A2:A5.
OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0) is A1:A4.
SUM(OFFSET(Table1[[#Headers],[ID]]:Table1[@ID],-1,0)) is SUM(A1:A4) = 3 because A1 and A2 don't contain numbers, A3 = 1 and A4 = 2.
The entire formula returns 3 + 1 = 4.
Etc.