The style of diamond cut referred to as emerald cut is made up of rectangular or square facets.  The diamond cutter has more flexibility in the shape of emerald cut that is produced as the proportions for this style of cut are not as rigid as those found in round brilliant cuts.  Thus you can find emerald cut diamonds of similar carat weights which look significantly different.  For example emerald cuts can be quite squarish in shape, other times they can be long and rectangular.  Which shape you choose is down to personal choice.  

The term emerald cut derived it's name from the cutting style used on the gemstone, emerald.  This particular cut was thought to intensify the green colour of the gem.