You can have many aliases pointing to your real email address. These allow you to give different addresses out to different people, and you can automatically sort incoming mail based on the address the person used. These addresses all have your email address in them. For example, you could subscribe to a news mailing list at email@example.com, a chat list at firstname.lastname@example.org, and for junk mail at email@example.com. All mail to these addresses will be delivered directly to your inbox. Just start using them as if they were your normal email address.
You can also have an entirely different address, so in addition to firstname.lastname@example.org, you could be email@example.com as well. Contact the administrator to set up those sorts of aliases. If you have a domain, you can set up your own aliases without asking the administrator.