The blending or fusing of the two notes in an interval or the many notes in a chord into a sound that seems to be 'at rest'.
It is one pole of the continuum of musical sonance, the other pole being described as "dissonance".
While the music of many different cultures exhibits consonace (to varying degrees) in its harmonies or melodies, the interplay between consonance and dissonance is consciously used as an important feature of European music and other styles derived from it. Dissonance seems to imbue music with a sense of goal-orientation, by seeming to propel harmonic progressions on, towards intervals or chords which are consonant, and which thus become goals to be reached.
While historically many theorists have used (and many still do use) the terms "consonance" and "dissonance" to refer to absolute psycho-acoustic phenomena, most modern tuning theorists prefer to limit the use of those terms to refer to relative perceptions which are a result of musical context, reserving the concept of accordance for the absolute psycho-acoustic phenomena; thus, the modern equivalents would be concordance and discordance.