Gmail allows dot characters in your email address, but ignores them when you send email to a Gmail address. So email@example.com and firstname.lastname@example.org are essentially the same email address. However, StackExchange treats these two email addresses as different addresses for the purpose of having a StackExchange account. So if you created your account under the name email@example.com , you cannot log in with firstname.lastname@example.org as your StackExchange account name.
I have a tendency to forget whether or not I used my dot character when I sign up for something, and I hate it when a website (1) uses email addresses as user IDs (a terrible practice, honestly) and (2) actually cares about dot characters. So it would be super cool if I could log in whether or not I put the dot character in my login email address.
I suspect that this is technically infeasible, but at least it will remind users to remember to use the proper email address when logging in.