to take up: to lift or receive something upward, or to pick a person or thing up and take it along
At its core this verb joins the ordinary word for taking or receiving (λαμβάνω) to the idea of upward or onward motion, so it always pictures picking something up and moving it: up into the air, up to heaven, or up onto a road or a ship. Which direction the "up" points is set by the scene, not by the verb.
Its most famous use is for the ascension. Jesus "was taken up" into heaven, always worded so that God, unnamed, is the one doing the lifting. The same picture describes the sheet full of animals in Peter's vision being drawn back up out of sight.
Elsewhere the word is thoroughly down to earth. It is what a ship's crew does when they take a traveler aboard, what soldiers do when they collect a prisoner for the road, and what Paul asks for when he tells Timothy to pick up Mark and bring him along. In a battle image it is taking a weapon in hand, as when a reader is told to take up the shield of faith. A near neighbor, αἴρω, leans toward lifting up or carrying away, while this verb leans toward taking something up in order to carry it onward.