A distribution list is another email address associated with your account (like an alias) but where email sent to that address is distributed to a number of users. This is commonly used for emails that regularly need to be sent to an internal department (eg. email@example.com) or to an external group of users (eg. firstname.lastname@example.org).
Distribution lists are only designed for groups of users that don't change regularly, and for email addresses that you know will exist. They are not designed for public mailing lists (there's no way for people to subscribe or unsubscribe) or for sending bulk emails like newsletters (there's no way to detect which addresses bounced and no way for users to unsubscribe).
The email addresses used for a distribution list are stored in the address book of the account where the distribution list is created.
So to create a new distribution list, first go to the address book and create a new address book group. Then add any addresses you want to the group (or use the upload feature to upload an address list into the group). Then go to the distribution lists screen, create a new distribution list, and assign the address book group to it.
To learn more about address book groups, see the Address Book Groups page.
Normally an email sent to the distribution list address will be distributed to all the recipients, regardless of where the email came from (internally or sent from an external address).
The "Internal" option on a distribution list allows you to limit the list to only accept email from internal users. Currently this means "internal to all FastMail" users, though this may change. This still significantly reduces the potential problem of spam being sent to the distribution list.