Any note or phrase where the rhythmic emphasis (attack) or accent(s) fall on the downbeat(s) (beats 1,2,3 and 4 in * time) of a measure is considered non- syncopated.
Therefore a note or phrase is syncopated when the attack or accent(s) fall on the "offbeat" (anywhere other than the downbeat).
Here is an example of a highly syncopated rhythm, e.g.:
This beat features a syncopated bass drum rhythm.