Do not delete the anonymous user.
The anonymous user is a very important user in PHPBB3. This is the profile that is used by non-logged in members and guests. This is not a user that logs on anonymously nor can anyone log into that profile. You do not want to delete this user as there is no way to recreate this user so it works correctly because of the built in settings which will be gone if the user is deleted.
This user is the only user in the guest group, and therefore gives guests the access or blocks their access according to how you set the groups access on the board and on the forums.
If you do not override users choice of style under Board Settings but allow users to pick their own style from a selection, the anonymous user is important because you can set on this user what style you want guests and non-logged in members to see until they log in and see the one they picked. To do this just go to Manage Users in the advanced ACP and tick the box next to the anonymous user and click submit. This will take you to the anonymous users profile and you would select preferences in the overview drop down menu and set the default style for the anonymous users there.
Do not add any other groups then the guest group to this user nor adjust the individual permissions so you do not accidentally give them global permissions to access the UCP or Private Messages or other things that could cause difficulty for the forum.
The roles usually applied to the quest group, and therefore to the anonymous user, are usually no access or read only. Guest posting is turned off across the network so even giving the anonymous user settings to post or create a topic will not work.