To waver is to move unsteadily back and forth — a candle flame wavering in a draught — and then, by extension, to be unsure, to nearly change your mind. So unwavering means holding perfectly steady: not moving, not weakening, not doubting.

It is used for things that could easily wobble but don't. Unwavering support, unwavering loyalty, unwavering belief, an unwavering gaze, an unwavering voice. Behind it there is always a pressure the person is standing against — bad news, criticism, years of waiting. That is what makes it a compliment rather than a description: an unwavering friend is one who stayed when staying was hard.

The word is fairly formal and warm. You find it in speeches, obituaries, thank-you letters, and news writing about someone admirable. In daily speech people say "she never gave up on me" or "he was always there".

It has a physical use too, and learners often forget this one: an unwavering stare or an unwavering hand simply means it did not shake. A surgeon's unwavering hands. Someone who looks at you with an unwavering gaze is not blinking or looking away — which can feel comforting or a bit frightening, depending on who is looking.

One honest note: because it praises so heavily, politicians and companies use it a lot, and it can start to sound empty. "Our unwavering commitment to our customers" often means nothing at all.