If you are using X11 forwarding, the local X server to which your forwarded connections are eventually directed may itself require authorisation.
Some Windows X servers do not require this: they do authorisation by simpler means, such as accepting any connection from the local machine but not from anywhere else. However, if your X server does require authorisation, then PuTTY needs to know what authorisation is required.
One way in which this data might be made available is for the X server to store it somewhere in a file which has the same format as the Unix .Xauthority
file. If this is how your Windows X server works, then you can tell PuTTY where to find this file by configuring this option. By default, PuTTY will not attempt to find any authorisation for your local display.