to come to someone's aid in trouble: to help by rushing to the rescue, in time and to real effect
At its core this word means to come to the aid of someone in trouble and actually rescue them, not to stand by with mild assistance. The old picture behind the word is a person running toward a shout for help, and even after that image faded into ordinary speech, the sense of urgent, effective rescue stayed with it.
In everyday Greek it was the natural word for troops rushing to reinforce an ally in battle, for a doctor stepping in to treat the sick, and for someone defending another in court. In each case the help is timely and it works: the ally is relieved, the patient is treated, the accused is defended.
The Greek Old Testament gave the word a deeper charge. It became the standard word for God rescuing his people, so much so that the Psalms repeatedly call God the one who helps, a title that stands right beside "savior" and "deliverer." The New Testament inherits that charged sense. It is heard in the desperate cries brought to Jesus, a father pleading for his son and a mother for her daughter; in Paul's quotation of Isaiah that God "helped" his servant; in the letter to the Hebrews, which makes Christ the one able to help those being tested; and even in the strange scene where the earth itself comes to a woman's rescue. The related noun for a helper (βοηθός) and the noun for the help itself (βοήθεια) carry the same weight, and the whole family answers to the Hebrew verb for helping (עָזַר).