The image shows the acceleration (orange arrow) of a planet revolving around the sun. The acceleration points from the planet to the sun.

This suggests that the sun has something to do with the planet's motion. Newton suggested that the sun is exerting a force on the planet called gravitational force and stated in his second law of motion that this force is proportional to the planet's acceleration.

For the acceleration to be pointing towards the sun and for Newton's second law to be true, the acceleration must be defined in a certain way. Acceleration must be defined as a vector and cannot be defined as the time-rate-of-change of speed, a scalar. Instead, acceleration is defined as the time-rate-of-change of velocity, a vector.

Because of the essential role of acceleration in Newton's second law of motion, a clear understanding of the definition of acceleration and what the definition entails for acceleration is very important. E.g., how can one understand that this definition implies that in the elliptical motion of a planet the acceleration always points to the sun?