A custodial sentence means the offender is removed from society-unable to commit crime for duration of sentence. Used as a means of protecting the public.
Change the offender into a better person via treatment programmes etc. Offenders should leave prison better adjusted to and ready to take their place in society.
Make the offender pay an eye for an eye. Many people see this as the primary function of imprisonment. Suffering is to be proportionate to the seriousness of the crime.
Put the offender off committing further crime, AND put other people off criminal behaviour by showing the negative consequences. Should prevent individual from reoffending the same crime.