Well, it's when the seed cavity in the centre of the courgette starts opening up. If you cut a courgette open crossways the flesh should still be solid all the way through. Once it starts to go fibrous and stringy in the centre, it's a marrow. You usually have to scoop this bit out when you prepare a marrow. So if a given courgette seems light for its size, it's a marrow.
And maturity has nothing to do with size btw. Different varieties of courgette plant produce different sizes of courgette/marrows. There are varieties which only produce mini courgettes and varieties which are bred to produce giant marrows.