A mirror curve is a mirror-image of the original curve.
Curve used to create a mirror curve
When you turn on the Mirror button, or while a mirror curve sub-object is selected, a rollout with the mirror parameters appears. Also, a gizmo (yellow by default) indicates the mirror axis.
The Mirror Axis buttons control the direction in which the original curve is mirrored. The Offset controls the mirror’s distance from the original curve. This parameter is animatable.
You can't transform the mirror curve directly (this simply transforms the mirror curve and its parent curve at the same time). You transform it by transforming its gizmo. By using transforms you can mirror about an arbitrary axis, rather than one of the Mirror Axis presets. When you transform a mirror curve, you are actually transforming the mirror plane, so Rotate has the effect of rotating the plane about which the curve is mirrored. (This is like rotating the mirror gizmo in the Mirror modifier.)
3DS MAX creates the mirror curve. A gizmo (yellow by default) indicates the direction of mirroring. Transforming the mirror curve’s gizmo changes the orientation of the mirror, letting you mirror along an axis that isn’t aligned with a local coordinate axis.