A hemiola is a musical term which describes a feeling of one time signature while you are in another. This is really, when you boil it down, a kind of syncopation. It is commonly found in latin musics as well as in Jazz, which is no suprise because both musical styles use syncopation frequently. One famous example that is accessible to most people is from West Side Story. The song "I want to live in America" uses a hemiola when Maria is singing "I want to live in America" the word "America" is split up over a hemiola. It is a halftime feel of three over a regular feel of three. I want to live in AMER-EE-CAH, those 3 syllables are the three beats of the hemiola.