Why is the threshold between human embryo and human fetus defined as 8 weeks after fertilization?
An embryo is called a fetus at a more advanced stage of development
  and up until birth or hatching. In humans, this is from the eighth
  week of gestation. However, animals which develop in eggs outside the
  mother's body are usually referred to as embryos throughout
  development; e.g. one would refer to a chick embryo, not a "chick
  fetus" even at late stages.



wikipedia - embryo


I can answer what "more advanced" means with the following 2 pictures. I think you can see the difference. (Real photos were too disgusting for me.)




Figure 1 - 7th week embryo - source





Figure 2 - 8th week fetus - source


For the sake of blind people and google, the 8th week fetus has a face and a human form, while the 7th week embryo doesn't.


  From the 10th week of gestation (8th week of development), the
  developing organism is called a fetus.
  
  All major structures are already formed in the fetus, but they
  continue to grow and develop.
  
  Since the precursors of all the major organs are created by this time,
  the fetal period is described both by organ and by a list of changes
  by weeks of gestational age.
  
  Because the precursors of the organs are now formed, the fetus is not
  as sensitive to damage from environmental exposure as the embryo was.
  Instead, toxic exposure often causes physiological abnormalities or
  minor congenital malformation.



wikipedia - prenatal development


So the scientific explanation of the threshold is that the precursors of all the major organs are created by that time.