Once you have marked the region, you need to transfer the text to the kill ring by either cutting or copying it.
Cutting text moves it from the current buffer into the kill ring, and deletes it from the current buffer, whereas copying just places a copy of the text in the kill ring.
Command+Xto cut the text.
Command+Cto copy the text.
Notice that these commands transfer the selected text to the Common LispWorks clipboard as well as the kill ring. This is so that the selected text can be transferred into other tools, or even into other applications.