a child: someone born to a parent, son or daughter, and by extension anyone belonging to a parent-like bond
At its core this word means a child in the simplest sense: a son or daughter, one who was born to a mother and father. It looks back to birth itself (it comes from the verb for giving birth), so it pictures a child as offspring rather than as a young person of a certain age. From there the New Testament stretches the word naturally outward.
Because a child is the one who comes from a parent, the word reaches past the immediate family to descendants in general, the whole line that springs from an ancestor. And because the parent-child bond is the warmest and most binding human tie, an older teacher or apostle will call a younger follower his child, claiming that same closeness and responsibility without any blood relation.
The most far-reaching use is spiritual. Believers are called the children of God, born into His family, and the same pattern produces a Hebrew turn of phrase where being a child of something marks the quality that defines a person: children of light, children of wrath, children of the promise. In every case the thread is the same, a child shows who or what it came from.