If something invariably happens, it always happens — there is no exception, or none the speaker is willing to allow. If a claim is invariably true, it is true every time. The word is a bit formal; in chat people usually say always. Though actually speakers often use it with a little heat or humour (He is invariably late) rather than as a scientist’s “one hundred percent.” It does not mean “in many different ways” — that would be variously — and it is stronger than often or usually. Put it before the verb or adjective it tightens: invariably arrives late, invariably right. If you only need a simple word, always will do; invariably adds a slightly bookish, “you can count on this, for better or worse” feel.