They say you can take any cylinder shape container, a bucket or jar etc and as long as the diameter is the same through out all you have to do is measure the amount of water at the bottom to get a total.
They are right, if you measure the
depth of the water at the bottom as Mattk says. But it doesn't even have to be a cylinder: anything with vertical sides will do, like a box.
Problem comes when you try to measure depth down to 0.01" in the bottom of a can or box, so it's best if you can funnel the rain you collect into a narrower container where it's easier to measure small amounts (like a CoCoRaHs gauge) or into a tipping bucket gauge - and that's where the math comes in

And speaking of math: over here we measure rain in millimetres (mm) but in, e.g., Belgium they measure in litres/square metre (l/mē). The number you end up with is exactly the same.