Merengue is a style of music which comes from the Dominican Republic.
There is a strong and (depending on the song)fast beat which makes dancing it different to its counterpart Bachata (the two styles tend to express different feelings, i.e. Merengue has the more party feel while Bachata is very romantic)
This strong beat is expressed in the steps (and hip movements) which you can see here:
I love the fast beat, when music is running at 120 bpm (beats per minute) and over you can really get drawn into the music.
I've got several favourite songs,
firstly let's listen to Elvis Crespo. His song Suavemente was a big hit and helped garner popularity for Merengue:
Check out Oro Solido as well. Here's their song Abusadora: