A socket card is a general card that does not have any device-specific hardware. E.g., a TQFP-64 socket card can be used for all devices that come in a TQFP-64 package, regardless of the pinout.
A routing card is a device-specific card. It routes signals between the STK600 motherboard and the socket card. Note that several devices may use the same routing card if they share the same pinout.
A set of spring-loaded connectors makes the connection between the motherboard, routing card, and socket card. Clips or screws hold the stack of cards together.
In addition to the socket and routing cards included in the kit, there are several add-on packs available to expand the part support for the STK600. See section Device Support page to get an overview of the different socket and routing cards.