the hand: the body part, and by extension the power, agency, and ownership that a hand stands for
At its core this is the ordinary word for a hand, the body part Jesus stretches out to heal, the hands raised in prayer, the hands the risen Lord shows his disciples. Most of its uses are exactly that plain and physical.
The wider senses all grow naturally out of the literal one, because in the ancient world the hand was what a person acted, gripped, gave, and held with. So the same word that means a hand also stands for what a hand does (work and agency) and for what a hand holds (power, control, and possession). To do something "by the hand of" someone is to act through that person, and to fall "into the hands of" someone is to come under that person's power.
These are shades of one idea, not separate words. Whether the text means the literal hand or the power it pictures is usually clear from the setting, and the line between them is often deliberately soft: the hand is present precisely because it is the visible sign of someone's reach and strength.
The most charged use is "the hand of the Lord," a phrase carried straight over from the Hebrew Scriptures. It names God's active power at work, whether to save, to build, or to strike, and it keeps the vivid bodily image even though God has no body.