Harmonies convey different emotions, sensations, and expectations. The tonic provides stability and familiarity. It is the key’s home from which we journey and eventually return. The dominant provides contrast to tonic; a tension that builds an expectation of resolution.
The interplay between these two harmonies is the foundation of tonal music, and entire phrases can be built from just these two harmonies. Understanding the role tonic and dominant play in a given musical passage is one of the central components of music theory.
The vast majority of tonal compositions end on tonic (i.e., I, the harmonic namesake of the key) because the tonic represents home, stability, and finality. Similarly, it is a common harmony on which to begin a piece.
Tension is caused by scale degrees and harmonies that imply resolution back to tonic. The leading tone (i.e., ^7) has the strongest pull back to tonic, particularly when it is in an outer voice and thus more prominent. Both vii° and V have the leading tone as part of their chord structures—it’s the root of vii° and the third of V. These harmonies also contain ^2, which tends to want to resolve down to ^1, and the V7 contains ^4, which wants to resolve down to ^3. The scale degrees that are not stable and imply resolution are called tendency tones. Proper voice leading and tendency-tone resolution dispels tension in the music. Lingering on dominant harmonies or leaving tendency tones unresolved creates musical tension and a longing for resolution.