Motion can only be described relative to a chosen reference frame. In one dimension, an object's position can be represented by a coordinate $x$ on an axis.

Position

The coordinate tells where the object is relative to the chosen origin. A negative position does not mean a negative distance; it means the object lies on the negative side of the coordinate axis.

Displacement

If an object moves from initial position $x_i$ to final position $x_f$, its displacement is

$$\Delta x=x_f-x_i.$$

Displacement contains direction through its sign. Moving from $x=2,\mathrm m$ to $x=-1,\mathrm m$ gives

$$\Delta x=-3,\mathrm m.$$

Distance travelled

Distance travelled measures the total length of the path and is always nonnegative. Displacement depends only on the endpoints.

An object that walks $5,\mathrm m$ away from its starting point and then returns travels $10,\mathrm m$ but has displacement

$$\Delta x=0.$$

In several dimensions, the same idea is represented by a position vector and displacement is the vector difference between final and initial positions.