Basically if you cross a double gene blue egg layer such as a good Cream legbar, over a brown egg layer, as long as the brown egg is not too dark you will get green or "olive" eggs.
Blue eggs have shells which are blue thoughout the shell, so if you peel away the inner membrane the shell colour will be the same as on the outside. Brown eggs are white (or almost) shelled eggs with a brown coating deposited just before lay, so the brown coating over a blue shelled egg makes for a green or olive coloured egg, depending on the depth of colour of the brown pigmentation
It is not a "breed" as such and will never breed true. It is generally a first second or third cross. But they lay lovely eggs which really add interest to an egg box