Position
Position is the location of an object, described as a distance and direction from a reference point.
Definition
Position is where an object is, described by how far it sits from a reference point and in which direction. On a number line, position becomes a signed value: positive on one side of the origin and negative on the other, and a change in position over time is what we call motion. In three dimensions, position is a vector $\vec{r}$ drawn from the origin of a coordinate system to the object, with components $(x, y, z)$. Its magnitude $|\vec{r}| = \sqrt{x^2 + y^2 + z^2}$ is the straight-line distance from the origin. The position function $\vec{r}(t)$ contains all the kinematic information about an object, because velocity and acceleration are simply its time derivatives.
Example
Your desk might be three rows back from the whiteboard and two seats from the window, and that description tells anyone your position in the classroom. On a track, set the starting line as $0\ \text{m}$ with east positive: a cart at $+12\ \text{m}$ is $12$ meters east of the start, a cart at $-4\ \text{m}$ is $4$ meters west, and the two carts are $16\ \text{m}$ apart. In two dimensions, a drone hovering at $x = 30\ \text{m}$, $y = 40\ \text{m}$, $z = 0$ relative to its launch pad is $\sqrt{30^2 + 40^2} = 50\ \text{m}$ from the pad, at an angle of $\tan^{-1}(40/30) \approx 53^\circ$ from the $x$-axis.
Key Insight
A position needs both a distance and a direction; saying "5 meters away" is not enough, while "5 meters north of the door" is a full position. Position is also different from distance: distance is how far something traveled, and position is where it ended up, so a runner who completes a full lap has zero change in position but a large distance. On a position-versus-time graph, the slope is velocity and the curvature reveals acceleration. Learning to read those graphs is the fastest route to understanding one-dimensional motion.