Im dating a latin guy and I love the music. Would just like more clarity on the music im enjoying so much. thanks.
Merengue and Bachata are from the Dominican Republic.
Merengue is a two step dance that people often compare just to walking or marching. By increasing the amount of bedn in your knees as you step, you increase the hip motion. It is the same hip motion as when you walk, just magnified.
http://www.youtube.com/watch?v=on4V1KN_Iuw
bachata is similar to salsa in that you take three steps, but rather than pausing on the 4th beat, you do a sort of pop with the hip. Tje dominicans invented it and are the best dancers. Other poeple ahve taken the basic idea but miss the subtlties of the dance (IMO).
Dominican dancing
http://www.youtube.com/watch?v=se6DzR6V6sY
http://www.youtube.com/watch?v=Hbn7lYVgYxs
Foreigners dancing bachata tend to have a very exaggerated style
http://www.youtube.com/watch?v=SyaxbEcvu9k
Salsa is a bit more complicated because various groups claim to have "invented" salsa. Salsa is not actually a rhythm but is a commercial term that was first used in the 1970s in the US to market what was often called "Latin Jazz" at that time. Essentially salsa is a mixture of the Cuban music styles son, guaracha or mambo with other musical elements such as jazz, rumba, plena and pop. In Cuba they also have mixed with funk. Since the word was first used in the US you can say salsa comes from New York Since salsa is all based on Cuban music styles you could say it’s Cuban. Salsa music sounds slightly different in different countries but it’s all based on the clave, a synchopated rhythm. You could say that "salsa" has different flavors because each country adds their own particular "spices" to the music but the base is still son or guaracha. The main salsa music producing countries are: The US (New York and Miami), Cuba, Puerto Rico, Colombia and also Venezuela. But there are also salsa bands all over Europe and even in Africa and Japan.
The basic rule of salsa dance is that it is danced three steps followed by a pause or a tap on the 4th beat. Salsa dance differs from country to country just like the muisc does.
Cuban salsa dance (called casino) is danced in a rotational patter with the couple moving as if they are following the edge of a circle with an axis bewteen them. It’s less flashy and more about moving your body and the moves are usually tangly, twisty moves. Notice the heavy funk elemnt in the Cuban salsa music as well. This couple also dances some afro-cuban rumba at times when they separate.
http://www.youtube.com/watch?v=-30RzT2wn64
New York Salsa – Dancing is a straight line back and forth. Lots of spins, arm styling and when the couple separates they do step patterns called shines. The preferred music of New York dancers is the classic 1970s New York music.
http://www.youtube.com/watch?v=BTIhekjRE1E
LA Style is also danced more or less linera. It is much more flashy with lots of dips and acrobatcics. Very much a "show" as you might expect from LA. They tend to have somewhat more open musical taste. There is no LA style salsa music. This style was "invented" very recently by the Vazquez brothers who moved to LA from Mexico.
http://www.youtube.com/watch?v=9vbYn9iJ7GM
Cali Style Salsa (also called Colombian style) has a very unique type of footwork from boogalu. They tend to like fast music and I expect they like Colombian salsa music a lot. This couple does alot of flashy moves that they may have picked up at a salsa congreso.
http://www.youtube.com/watch?v=IEuhOR_Arh8
There is also a type of salsa called Rueda de Casino (casino wheel) invented in the 1950s in Cuba. It’s danced all around the world now. It is similar to square dancing in that you have a person calling out the moves. In Rueda the caller is one of the dancers. The couples perform the moves in unison and very often switch partners at the end of the move. But you never know what move the caller will call next. If you and your boyfriend knew the names of all these moves you could join in this rueda and it would work perfectly even if you’ve never met the people before.
http://www.youtube.com/watch?v=rrl1uAGw8yw
by GINO DJ EXCLUSIVO BACHATERO
DANIELE TI VOGLIO TROPPO BENE
Monchy Y Alexandra Official Video, 
This is a free style demonstration of Bachata Moderna by Juan Ruiz and Samantha Cilia, from Bachateros.