Anatomy and expression are both very important components of art. One makes the character look realistic, the other makes it look more lifelike.
Anatomy is fairly simple once you get proportion down. It's a good idea to use circles and shapes to help you with this. It's especially good in learning how to differentiate between the male and female form. I do it by using basic shapes: a triangle for a male, and an egg for a female, featured below.
Remember that men and women are not physically built the same! The mass of a male is centered around the shoulders, while the mass of a female is mostly centered around the waist. The shoulders should be the widest point on a male, and the hips should be the widest point on a female. Below are basic circle drawings of the male and female form... with the triangle and the egg bolded out a bit to show you. All too often I see people use the same basic body form for male and female characters, either drawing females with no mass in the hips, or males with too much mass in the hips and not enough in the shoulders.


You should also remember to shape your characters according to their personalities. A beggar should be lean. A warrior should be muscular. A mother might be drawn as a bit on the plump side. The way your character is shaped will determine a lot about how people view them. If they all look the same, you won't get much of a reaction. Also remember that in real life, we all aren't perfect looking... neither should your characters be.
Expression
Expression is the first and most basic way humans read one another, and it's also the first and most basic thing about any character. If your character is incapable of showing emotion he won't be very exciting.
You can divide character expression into three parts. Each part taking a large or small role in the character. Facial expression is the most important -- about 60% of the character expression is right there in the face. Another 30% is in body language, that is, how the character is posed and such. The final 10% is in the hands. Each is important, and a mastery of all three is the true key to having the most lifelike characters.
Facial expression is the easiest. Learn how to use the eyes, ears, nose, and mouth to show how the character is feeling. Narrowed eyes, a pouty mouth, flared nostrils, or laid back ears are all easily read flags that indicate how a character is feeling. Use all of these to your advantage.
Body poses are also important... but less so. Someone feeling sad might have tears in their eyes and a downcast look... but MORE might be suggested by perhaps having them sitting down, arms draped over folded up legs. Hugging oneself, jumping for joy, and going rigid with anger are all good examples of expressive body language.
Hands are the final component. Hands are probably the hardest part of the human body to learn how to draw, both in proportion and complexity, but it's well worth it. The very shape of the hand can show a lot about the character. Are the fingers long and slender? Or are they stumpy and knotted? Pointing, gesturing, and grasping are all personality and expression indicators as well.
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