Definition
A human embryo is the first stage of human developement.
It is formed by the fusion of the male gamete (spermatozoon) and female gamete (ovum). This is called fertilization and usually occurs in the proximal portion of the female reproductive tract.
Controversies
There are several controversial issues involving human embryos.
IVF: Traditionally, fertilization occurs via insemination of a female by a male during marital relations. However, reproductive science has created many advances in fertilization, allowing infertile couples to have their own biological children. In vitro (in glass) fertilization allows for the creation of embryos in a laboratory. This embryo is then surgically implated in the mother. This is also know as artificial insemination. The first so-called "test tubee baby" was born in the 70s and is now a healthy female adult. There has been a great deal of controversy about this practice, and there are many interesting moral/religious viewpoints on the topic. Many see IVF as a way for couples to help fulfill God's commandment to be fruitful and multiply, others see it as science invading the territory of natural marital reproduction.
Abortion: abortion interrupts the development of an embryo into a living baby separate from its mother. This issue is addressed in depth elsewhere.
Stem cells: also addressed extensively elsewhere.