The Assigned to [assigned_to] field is a reference field type that points to the Users [sys_user] table. This field is generally used to designate a user to work on, or be responsible for the task. By default, this field has a reference qualifier (role=itil) set on its dictionary record that prevents any non-itil user from being assigned to a task. You can override this reference qualifier on tables that extend task though, as the Project Task and Service Order tables do, if you have the relevant plugins installed.

The Assignment group [assignment_group] field serves pretty much the same purpose. The reason for having both, is that a workflow might automatically assign a certain type of task ticket to a group, but you would not want to hard-code a specific user to be responsible for such tasks (what if that user left the company?), so you'll generally assign a ticket to a group, and have a BA, manager, or the itil users themselves assign tickets to individual IT workers.

By default, the Assigned to field is also set as Dependent on the Assignment group field. The result of this, is that only users who are in the assignment group can be chosen in the Assigned to field.