'Higher' in the Bible

It was fitting for us to have such a High Priest [perfectly adapted to our needs], holy, blameless, unstained [by sin], separated from sinners and exalted higher than the heavens;

But as it is, Christ has acquired a [priestly] ministry which is more excellent [than the old Levitical priestly ministry], for He is the Mediator (Arbiter) of a better covenant [uniting God and man], which has been enacted and rests on better promises.