Dissonance, resolution, and suspense can be used to create musical interest. Where a melody or chordal pattern is expected to resolve to a certain note or chord, a different but similarly suitable note can be resolved to instead, creating an interesting and unexpected sound. For example, the deceptive cadence.
A dissonance has its resolution when it moves to a consonance. When a resolution is delayed or is accomplished in surprising ways—when the composer plays with our sense of expectation—a feeling of drama or suspense is created.
The concept of "resolution", and the degree to which resolution is "expected", is contextual as to culture and historical period. In a classical piece of the Baroque period, for example, an added sixth chord (made up of the notes C, E, G and A, for example) has a very strong need to resolve, while in a more modern work, that need is less strong - in the context of a pop or jazz piece, such a chord could comfortably end a piece and have no particular need to resolve.
An example of a single dissonant note which requires resolution would be, for instance, an F during a C major chord, C-E-G, which creates a dissonance with both E and G and may resolve to either, though more usually to E (the closer pitch). This is an example of a suspended chord. In reference to chords and progressions for example, a phrase ending with the following cadence IV-V, a half cadence, does not have a high degree of resolution. However, if this cadence were changed to (IV-)V-I, an authentic cadence, it would resolve much more strongly by ending on the tonic I chord.