As mentioned in one of the previous Salesforce interview questions, a profile will ultimately control access to which records a user has in a Salesforce org. No user can work on the Salesforce org without being assigned a profile. The Profile is therefore mandatory for every user.
Role however is not mandatory for every user. The primary function of the Role/ Role hierarchy is that it allows higher level users in hierarchy get access to records owned by lower level users in the hierarchy. An example of that is Sales Managers getting access to records owned by Sales Reps while their peers do not get access to it.