The existence of the soul is heavily debated in the first place, and its definition varies greatly from party to party, though everyone believes that everyone else's definitions are wrong. It is generally agreed to be something possessed by every person, and that's about all. Therefore, the soul may or may not be any of the following:
1. The human mind, that is, that thinking thing lodged behind your eyes;
2. The essence of humanity;
3. The essence of that which makes a person good and decent;
4. The quality of sentience or human intelligence;
5. All of someone's personality or what makes them unique;
6. Some mystical version of a person that lives on after the body dies;
7. A spiritual concept, created by God (or the gods if you prefer) or a part of him;
8. The quality of being alive;
9. Anything else you can think of along these lines.
Note that it is also up for debate whether or not non-human animals, or for that matter, plants, have souls; feel free to adjust these answers accordingly.
Strangely, no one seems to suggest that animals have souls and humans lack them.
1. A Japanese term for animation.
2. In America, used to refer to a particular style of art common to Japanese animation and comics.
3. In America, also used to refer to Japanese animation as a whole. The Japanese approach to art and storytelling is distinctive, at least to Americans, and has earned anime quite a few fervent fans and as many detractors. Still, regarding "anime" as a genre is misleading; it's really just a medium, whose subjects encompass drama, comedy, action, children's entertainment, pornography, and what have you. As with any form of entertainment, some of it is good, some is bad, most is in between, and no one will ever agree on what titles are which.
The increasingly popular localization of anime in America is a subject of great controversy among its fans.