Flexible and extensive control over geometry: curves, surface, solids and meshes; transformation, model manipulations (rounding, solid operations, sweeping & lofting, trimming…). The focus is clearly NURBS geometry and to a lesser extent Mesh geometry. Subdivision modelling (as a hybrid between NURBS and meshes, from the user's point of view) is upcoming.
Attractive licensing, without subscription or forced yearly updates. They also have an open policy for educational users: low license, without usage or feature restrictions (even commercial work). Quite exceptional.
Rhino has file import and export convertors for a wide variety of CAD and design formats. Via plug-ins you can even expand this more.
Impressive versatility, esp. when adding the Grasshopper visual programming system (add-on). For architectural and BIM design, extensions and plug-ins are available to extend and improve the usability. That said, don't compare it directly with software like ARCHICAD or Revit, as they have a different purpose.
It took a few years to arise, but the Mac version is now becoming very usable and quite complete. Not for 100% as some plugins and features remain Windows-only.
No free student version (but license allows commercial usage even for EDU users).
Mac version does not support Grasshopper, so still need Windows version.
Could be better integrated in e.g. BIM processes (partly solved by add-ons).
When complex 3D geometric editing goes beyond what AutoCAD or SketchUp provide or when you want to use Grasshopper, this is the CAD system to use.
Complex geometric model creation, especially if smoothness and continuity are required.