If you enable ‘Paste to clipboard in RTF as well as plain text’, PuTTY will write formatting information to the clipboard as well as the actual text you copy. The effect of this is that if you paste into (say) a word processor, the text will appear in the word processor in the same font, colour, and style (e.g. bold, underline) PuTTY was using to display it.
This option can easily be inconvenient, so by default it is disabled.