How did paper size A4 derived?

Answer 1

All based on the standard A0 sheet size.
A1 is half size of A0, folded along its longer length.
A2 is half A1, folded along its longer length.
A3 is half A2, folded along its longer length.
A4 is half A3, folded along its longer length.
A5 is half A4, folded along its longer length.
and so on and so forth.

Answer 2

Try this explanation:
http://www.webopedia.com/TERM/P/paper_size_systems.html