When linked to a place or nationality it is synonymous with "indigenous", as in "Native American". Phrases like "native English speakers" are thus ambiguous, meaning either "native speakers of English" or "speakers native to England".
In biology, native means "of or from a certain place or region" and includes both indigenous and endemic species, contrasting with any of several terms meaning not native to a place: non-native, alien, adventive, or introduced.
to describe something running on a computernatively or in native mode means that it is running without any external support—for example, as opposed to it being running emulated.
Native operation system, native instruction set, etc., in application to a computer processor means that the corresponding item was implemented specifically for the given model of computer, as opposed to, say, emulation or compatibility mode.