How does a tonic chord function as a harmonic goal in a key?

In the system of tonality, the tonic chord functions as the primary harmonic goal—a focal point toward which all other notes and chords in a key gravitate. It serves as the point of departure and arrival for musical compositions, phrases, and sections.1234

The tonic chord achieves this status through its role in functional harmony, where chords are organized to create or resolve tension. The most significant mechanism for reaching this goal is the authentic cadence, which involves a progression from the dominant chord (built on the fifth scale degree) to the tonic chord.1256

The dominant chord exerts a strong "pull" toward the tonic because it contains the leading note—the seventh degree of the scale—which sits only a half step away from the tonic note. This gravitational pull is often intensified by using a dominant seventh chord, which incorporates additional dissonances that demand resolution into the stable, consonant tonic triad. Consequently, the movement to the tonic provides a sense of finality and structural resolution, acting as the musical equivalent of a period at the end of a sentence.36