The term native is an adjective, synonymous to "indigenous", referring to people whose origin is localized to an area —the term "native" always refers to a context to which the subject of the statement belongs.
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 correcponding item was implemented specifically for the given model of the computer, as opposed to, say, emulation or compatibility mode.