Embalming is a process by which bodily fluids are replaced with chemical preservatives that slow the natural decomposition process. 
The Civil War era sparked an interest in embalming which allowed the bodies of soldiers to be sent home for burial, and it became very common in the U.S. by the turn of the 19th Century. In many countries, embalming is rare and some religions, such as Orthodox Judaism, forbid it.
While there are no laws in any state that require embalming, some funeral directors insist on it if there is to be a viewing or if the body will not be buried within 48 hours. Refrigeration or dry ice can substitute for embalming in many instances if burial is delayed.
Ultimately the decision as to whether to embalm rests with the family.