Axis of rotation is a term used in many branches of engineering, mathematics and the sciences. It's used to describe a type of motion for objects existing in three dimensional (3D) space. It is an imaginary straight line drawn through a 3D object around which the object can rotate or spin. Models of rotation are used for both theoretical and practical applications.
Rotation around an axis can only occur in three dimensional space, meaning an object has length, width and depth. Objects in two dimensional (2D) space can rotate, but the rotation is around a point — either internal or external — on a flat plane, not on an axis. The image cannot truly rotate around an axis as it does not exist in all three dimensions — it has length and width, but no depth. If a 2D object is charted on a graph, it can be "rotated" around the X or Y axis, but this simply flips or reverses the image. The image is flat and would disappear at some point if spun through a full rotation around either axis.
In contrast, a 3D object can rotate around an axis but cannot rotate around an internal point. This would cause the object to rotate in many directions at the same time, along every line that intersects that point, and it would rip itself apart. Thus, a 3D object can only rotate around one line, or an axis. If a 3D object is moving around an external point, it is referred to as a revolution, not a rotation. For example, the Earth rotates on an internal axis and revolves around the sun.
Objects existing within 3D space can have more than one internal axis of rotation, but they cannot rotate around two such axes at the same time. For example, if the Earth has a new axis of rotation that is perpendicular to its original axis, it cannot spin in opposing directions on both axes at the same time. As it attempts to spin in both directions, it will find a balancing point between the two and create a third axis of rotation along that line.
Objects which cannot perform a full rotation or spin can still be considered as rotating around an axis. Ankles and knees, as well as mechanical parts and many other items, can perform limited rotation around a given internal line. As they are 3D objects, they are referred to as having an axis of rotation, even though the rotation itself is limited.