It depends slightly on the context.
In local authority services, a 'statutory' service is one the authority is required by law to provide and a 'non-statutory' on is one they can provide if they see fit. E.g. in LEA schools teaching English is statutory but teaching dancing is not - an LEA which did not provide English lessons in it's schools would be in trouble but it is up to them to decide whether to provide dancing classes. Similarly most councils choose to provide public libraries but these are not statutory.