Though dot (.) is a valid character in a gmail id, gmail never really uses that. Instead, it ignores the dot(s) in the email address. This means that, if your email id is firstname.lastname@example.org, you can login to the same account as email@example.com, firstname.lastname@example.org or any combination like that. Now that is not really an advantage. Nobody would want to login to the same account with multiple ids.
Creating aliases for your gmail account using this feature:
The real advantage is when using the same email account for different use and avoiding clutter by setting up labels based on the To: address of the email. I can, for example, give email@example.com to my friends and firstname.lastname@example.org to others. After that, all I have to do is, setup filters so that all mail for email@example.com get labeled with ‘Friends’ and sorting becomes easy. You don’t need multiple email accounts. The position of the dot can be changed or more dots included to create more and more aliases for your email address. The fact that gmail ignores dot in the email address was told to me by Razee Marikar.