Blender has two methods for model navigation using the viewport, namely turntable and trackball, with the default being turntable. When I use trackball instead, I can feel that something is changed, but I can't seem to be able to explain the difference to someone who has never tried it before. How can I explain, in a technical or non-technical manner, the difference between the two rotation modes?
I'm surprised at the analogy used in the wiki concerning Turntable. This is a turntable for scultping with clay. This lets you rotate around the vertical axis so you can see all sides and judge their proportions accordingly. This is why the mode is called
Trackball lets you rotate freely around a point in 3D space, this is like picking up the object with your hands and rotating it around until the point of interest is visible.
As per the wiki
By default, when you rotate the view, you are using the turntable method. For some users this is intuitive and for others it is not. If you feel you are having difficulties with this style of 3D window rotation you can switch to the "trackball" style.
With the Trackball style you are rotating the scene as though you are rolling your hand across a "trackball".
The Turntable style is fashioned more like a record player where you have two axes of rotation available, and the world seems to have a better definition of what is up and down in it. The downside to using the Turntable style is that you lose some flexibility when working with your objects. However, you gain the sense of up and down which can help if you are feeling disoriented. Of course you can always switch between the styles depending on what you are working on.
The only difference, as far as I can tell, is that Turntable rotation mode locks the viewport's Z axis orientation. Trackball doesn't lock Z orientation, and can be a bit confusing if we're not used to it.