Polyrhythm is the simultaneous sounding of two or more independent rhythm
Rhythm may be generally defined as a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions." This general meaning of regular recurrence or pattern in time may be applied to a wide variety of cyclical natural phenomena having a periodicity or...

Polyrhythm in general is a nonspecific term for the simultaneous occurrence of two or more conflicting rhythms, of which cross-rhythm is a specific and definable subset.—Novotney (1998: 265)

Polyrhythms can be distinguished from irrational rhythms, which can occur within the context of a single part
Part (music)
1) A part is a strand or melody of music played by an individual instrument or voice within a larger work. Parts may be referred to as an outer part or an inner part . Part-writing is the composition of parts in consideration of harmony and counterpoint...

; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm.
The terms polyrhythm and cross-rhythm are often used interchangeably.