The long and short of the article is that you can add a plus sign (+) after your e-mail address, and anything after the plus sign, and the mail will still reach you. This is because when delivering mails, Gmail ignores the plus sign and everything after it.
E.g. if your e-mail address is firstname.lastname@example.org, mails that are sent to email@example.com, firstname.lastname@example.org, etc, will still reach you.
The article describes a few good practical uses for such a feature.
To add on, Gmail ignores dots (.) in e-mail addresses as well. E.g. if your address is email@example.com, basically, it is also equivalent to firstname.lastname@example.org, email@example.com, etc. This is explained in https://mail.google.com/support/bin/answer.py?ctx=%67mail&hl=en&answer=10313.
Do keep in mind two things though:
1. Even though Gmail ignores the dots, you cannot have two successive dots; that would result in an invalid address. (E.g. my..firstname.lastname@example.org)
2. Hypens (-) and underscores (_) cannot be used in Gmail addresses.