Because vii is a diminished triad and therefore considered unstable, the progression from this chord to the much more stable tonic produces a strong sense of tension resolution. As shown in the example below, it functions as a sort of substitute for the dominant - being the same notes as a dominant seventh but without the root.
This example from a Haydn String Quartet shows the overlap in function between vii and V. The effect at the end of the first bar and beginning of the third is of dominant seventh to tonic, but strictly speaking the chord in both cases is vii, because there is no F in the chord.
The final example on this page shows a very common use of vii. The chord, in first inversion, passes between two tonic chords, with contrary motion in the outer voices.
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