Motion
Motion is a change in an object's position over time, measured against a chosen reference point.
Definition
Motion means an object is changing where it is: if something is in a different spot now than it was a moment ago, it is in motion. More carefully, motion is a change in position over time measured relative to a reference point, and scientists describe it using distance, displacement, speed, velocity, and acceleration. In formal terms, motion is captured by the time dependence of an object's position vector $\vec{r}(t)$ in a chosen reference frame. Its first derivative is velocity, $\vec{v} = d\vec{r}/dt$, and its second derivative is acceleration, $\vec{a} = d\vec{v}/dt$. Kinematics describes motion without asking why it happens, while dynamics connects motion to the forces that cause it through Newton's laws.
Example
A school bus pulling away from the curb is in motion because its position changes compared to the stop sign beside it. A runner who starts at the $0\ \text{m}$ mark and reaches the $100\ \text{m}$ mark $12.5\ \text{s}$ later changed position by $100\ \text{m}$, so she moved at an average speed of $100 \div 12.5 = 8\ \text{m/s}$. For a fuller picture, consider a ball thrown horizontally at $6\ \text{m/s}$ from a height of $4.9\ \text{m}$, which follows $x(t) = 6t$ and $y(t) = 4.9 - 4.9t^2$. It lands when $y = 0$, at $t = 1\ \text{s}$, having traveled $6\ \text{m}$ horizontally. The two directions are independent, which is why the motion is analyzed as two separate one-dimensional problems.
Key Insight
You can only tell something is moving by comparing it to something else: a passenger sitting still on the bus is moving compared to the road but not compared to the seat. Motion is relative in this sense everywhere. Earth spins and orbits the Sun, yet a book on your desk is "at rest" because you and the book share the same reference frame. Galileo's principle of relativity makes this precise: no experiment inside a smoothly moving cabin can detect uniform motion. There is no absolute rest frame, so "moving" always means "moving relative to something".