When run SnapGene may try to get in touch with our servers to register or check license details, check for updates, or send anonymous statistics. See Does SnapGene Send My Data to External Locations?
If SnapGene detects that a proxy authentication is required to access the internet then you will see the above dialog.
Enter your proxy login credentials to allow SnapGene to access the internet. SnapGene does not store the authentication details and they are only used until SnapGene is quit.