This option copies the name of the curenty selected attribute in the attribute list panel to the clipboard. You could also press CTRL-C for this.
The Copy Attribute Value option is only visible in the menu if the following conditions are met:
LEX can paste the copied attributes directely into another object! This is a very fast way to transfer attribute values between different objects.
You can read all about LEX's clipboard handling for attribute values in the according manual topic Copy and Paste of Attribute Values.