to serve someone by meeting their needs: to wait on them, look after them, or carry out a task on their behalf.
At its heart this word means to do something useful for another person, with that person as the one who benefits. It always points outward to someone served, and it carries the flavor of practical, often humble help rather than rule or command. The plainest picture is waiting on people at a meal, bringing the food and drink and seeing to the guests, and that everyday scene stands behind the wider uses.
From there the word stretches to any kind of personal care: providing for someone, supporting them out of one's own resources, looking after them in sickness, prison, or need. The same verb describes the women who supported Jesus and his followers, the angels who cared for him in the wilderness, and the friend who attends to a prisoner. Jesus uses it of himself when he says he came not to be waited on but to wait on others, turning a lowly word into the pattern of his whole life.
In the letters the word takes on a settled Christian use for service done within the church and for the gospel: gathering and delivering the relief money for poorer believers, using one's gifts to help the body, doing the work that later attached to the office of a deacon. The thread running through every use is the same. To serve in this sense is to spend yourself usefully for another, and the New Testament makes that ordinary act the shape of a Christian life.