A three-dimensional orientation can be described by composing three rotations about specified axes. The three angles used in such a convention are commonly called Euler angles or, in some conventions, roll, pitch and yaw.

A sequence, not just three numbers

The axis order is part of the definition. Rotating about $x$, then $y$, then $z$ generally gives a different orientation from applying the same angles in another order.

The complete rotation matrix is obtained by multiplying the component rotation matrices in the convention's prescribed order.

Gimbal lock

For particular orientations, two of the rotational axes represented by the angle convention can become aligned. The coordinate representation then loses one independent direction of instantaneous rotation.

This singularity is gimbal lock.

The physical orientation still exists; the problem lies in the chosen coordinates used to parameterize it.

Why Euler angles remain useful

Euler angles are intuitive for human-readable controls and for rotations naturally associated with named axes. Their singularities and order dependence become problematic when orientations must be composed, integrated or interpolated robustly.

Quaternions provide another coordinate representation of rotations that avoids this particular singularity.