Syncopation

In music, syncopation involves a variety of rhythms which are in some way unexpected which make part or all of a tune or piece of music off-beat. More simply, syncopation is a general term for "a disturbance or interruption of the regular flow of rhythm": a "placement of rhythmic stresses or accents where they wouldn't normally occur." The correlation of at least two sets of time intervals. Also known as an "Uneven movement from bar to bar".

Syncopation is used in many musical styles, especially dance music--"All dance music makes use of syncopation and it's often a vital element that helps tie the whole track together". In the form of a back beat, syncopation is used in virtually all contemporary popular music.

Syncopation can also occur when a strong harmony is placed on a weak beat, for instance when a 7th-chord is placed on the second beat of 3
4 measure or a dominant is placed at the fourth beat of a 4
4 measure. The latter frequently occurs in tonal cadences in 18th and early 19th century music and is the usual conclusion of any section.

A hemiola can also be seen as one straight measure in 3 with one long chord and one short chord and a syncope in the measure thereafter, with one short chord and one long chord. Usually, the last chord in a hemiola is a (bi-)dominant, and as such a strong harmony on a weak beat, hence a syncope.

Technically, "syncopation occurs when a temporary displacement of the regular metrical accent occurs, causing the emphasis to shift from a strong accent to a weak accent." "Syncopation is," however, "very simply, a deliberate disruption of the two- or three-beat stress pattern, most often by stressing an off-beat, or a note that is not on the beat."

In the following example, there are two points of syncopation where the third beats are carried over (sustained) from the second beats rather than missed. In the same way, the first beat of the second bar is carried over from the fourth beat of the first bar.  Play 

...
Wikipedia