n.
Function: preposition
Date: 1509
1 a ― used as a function word to indicate motion to or toward or situation at a higher point of <went up the stairs> b : up into or in the <was hid away up garret ― Mark Twain>
2 a : in a direction regarded as being toward or near the upper end or part of <lives a few miles up the coast> <walked up the street> b : toward or near a point closer to the source or beginning of <sail up the river>
3 : in the direction opposite to <sailed up the wind>