It occurs in a system with island platforms: where there is a single platform in between the two directions of travel, or two platforms between the tracks, connected by level corridors. In a cross-platform interchange, instead of the two opposite directions of a single line sharing an island platform, two similar directions of two different lines share it. In London's deep-level tube network, these usually occur in pairs for both directions of two lines. This allows for extremely quick and convenient interchange. The net effect is that the two lines, though they have completely separate operation from the point of view of the trains and the tracks, can be treated by passengers as branches of a single network.
Below is a simplified diagram of one such interchange at Oxford Circus tube station.