to get up: to come up from a sitting, lying, or kneeling position, and by extension to set out or to step forward to act
At its plainest this word names the bodily motion of coming up off the ground or out of a seat. A sick man gets up from his bed, a guest rises from the table, a mourner stands up to leave.
From that picture the New Testament draws two natural extensions. One is to set out: in a storytelling habit carried over from the Old Testament, a person gets up and goes, where the getting-up simply signals that the next action has begun (Mary got up and hurried to the hill country). The other is to stand up in a public setting, whether to speak, to give testimony, or to oppose someone, so that the word can describe a leader, a movement, or false teachers coming on the scene.
The same word also works the other way around: God or a person can cause someone to stand up, that is, bring a figure forward onto the stage of history. So Scripture says God will raise up a prophet like Moses, or raise up offspring to continue a family line. The action is still the basic one of bringing someone up and into view.