First lets define a courtyard. A courtyard would be outdoor space enclosed sufficiently by a building or structures to create a clearly defined area. Sometimes it can be an indoor space that is treated as if it is an outdoor space.
An underground courtyard could imply two different versions, as I see things. First, a courtyard depressed into the ground, or secondly, an enclosed space below the plane of your ground floor.
For the first version it may not seem any different from a traditional courtyard. The edges would be defined by walls of the edge. They could be sloped or vertical, but an occupier of the space may never know they are underground unless the edges were quite tall compared to the other dimensions of the courtyard.
For the second version, it would be an indoor space being used as if it were outdoors. Unless handled well most occupiers would probably identify it as an atrium or greenhouse than a courtyard unless it was large and tall.
In most cases the size and depth of the spaces would have a huge impact on the difference. As would the access to sky/outside. Either way try to avoid the concept of being at the bottom of a hole. Unless that was the concept.
Hopefully this helped.
MKDesign 