When something is unwavering, it is firm or unshakable. If you're a good hockey goalie, then you'll show an unwavering determination to keep the puck out of your goal.
Just as it sounds, the word unwavering refers to something that will not waver, wander, or go astray. Unwavering most often refers to mental determination, like an unwavering desire to marry the love of your life or an unwavering intent to become a doctor even though you faint at the sight of blood. Unwavering can also refer to something that remains steady, like the unwavering sound of a trumpet horn or the unwavering energy of a very enthusiastic rock band.