What is all properties of orthogonal axis (dq) axis?
The dq transform is mostly used in the analysis of synchronous machines.  The reference frame is fixed to the synchronous rotor.

The d-axis is aligned with the magnetic field of the rotor and th q-axis is orthogonal to the d-axis and the rotation.

You can imagine yourself rotating inside the machine, rotating at synchronous speed.  It makes it simpler to analyse some phenomena such the impact of transient loads on the rotor.  The rotor will now slowly swing from side-to-side from your reference, instead of speeding up and slowing down if you use a stationary reference.