to be sick: to suffer bodily illness or disease
This is the everyday medical use of the word. A person who is sick has lost the strength of a healthy body, so the same verb that means "to lack strength" is the ordinary New Testament way to say someone is ill. The Gospels use it constantly for the crowds of suffering people brought to Jesus, and the letters use it for named friends laid low by disease.
The range runs from a passing illness to being at the point of death. Lazarus, the official's son, Dorcas, Trophimus, and Epaphroditus are all described with this word, and in several of those cases the sickness is serious enough that death is near or has already come. So the verb does not by itself say how grave the illness is; the surrounding story supplies that.
When Jesus tells his followers to "heal the sick," or when the letter of James asks whether anyone is sick, this bodily sense is plainly in view. The cure or the prayer answers a physical condition.