The checkbox ‘Auto-copy selected text to system clipboard’ controls whether or not selecting text in the PuTTY terminal window automatically has the side effect of copying it to the system clipboard, without requiring a separate user interface action.
On X, the wording of this option is changed slightly so that ‘CLIPBOARD’ is mentioned in place of the ‘system clipboard’. Text selected in the terminal window will always be automatically placed in the PRIMARY selection, as is conventional, but if you tick this box, it will also be placed in ‘CLIPBOARD’ at the same time.