What are they?#

Quaternions are compact four dimensional values that can be easily interpolated between values (to rotate to another orientation via the most direct rotation).

To use them practically you don't need to understand them beyond that simplified description.

What aren't they?#

Quaternions are not Euler angles.
What this means:

What do they represent?#

Confusingly just as a Vector3 can represent a position or a direction, a quaternion can represent either an orientation or a rotation.
An orientation is a rotational placement, similar to position. transform.rotation is the global orientation of a transform.
A rotation is a manipulation of another orientation or rotation, similar to a movement vector.

Sadly, rotation is a general term and is used to describe both orientations and rotations.

The API#

Rotation construction#

Rotation modification and application#