The notional is purely a reference amount. For the vast majority of derivatives the notional amount is never exchanged (cross-currency basis swaps being a notable exception).
E.g a simple interest rate swap: I agree to pay you 2% per annum on a reference notional of 100m for 10 years, and in exchange you pay me libor referencing the same notional. At the end of first year let's say libor fixes at 1.98%. Hence I pay you a net 0.02% (2% - 1.98%) of 100m, i.e 20,000. We do this every year for 10 years.
It is just a way to hedge interest rate exposure - e.g I have borrowed 100m paying a Libor-linked interest rate and don't want to run the risk that Libor spikes to 10% or whatever.
There's nothing complicated about this, at least in principle. Derivatives just allow people to hedge out exposures they don't want.