Learn Russian: Здоровый человек не болен.

In Russian, the present tense of the verb "to be" is almost always left out. So, Здоровый человек (a healthy person) directly connects to не болен (not ill) without needing an "is" in between.

Why is the word for ill болен instead of the normal adjective больной?

Болен is a "short-form" adjective. In Russian, short forms are often used to describe temporary states or conditions, like being sick, glad, or busy. They act as the main description at the end of a sentence. If you wanted to say "a sick person" before the noun, you would use the regular long form: больной человек.

If we were talking about a woman, how would this sentence change?

The describing words would change to match the feminine gender. "A healthy woman is not ill" would be Здоровая женщина не больна. Notice how the adjective Здоровый changes to Здоровая, and the short-form adjective болен changes to больна.

Does человек mean "man" or "person"?

Человек means "person" or "human." If you want to specifically say "man" (as in an adult male), you use the word мужчина. Because человек is a grammatically masculine noun, the describing words around it (Здоровый and болен) take the masculine form, even though a "person" could be of any gender.