In true Blue Peter fashion, get a globe and a piece of string (and an adult if you need one).
Take two points on your globe, say, London and New York, and stretch the piece of string between the two. You will notice that the line the string traces between the two points doesn't always cut the meridians at the same angle. That is the great circle, i.e. the shortest distance between the two points.
If you make the surface of your globe flat (using whatever method), it is very unlikely that the line that you originally drew would be straight.
Rhumb lines: these always cut meridians at the same angle... so on the globe, look at the equator. It cuts each meridian at 90 degrees. And look at the tropic of capricorn... same deal.
Hope that helps.