Connected lines are lines where the end point of one line is the start point of the next line and where the connection is "smoothed".
For example the following XAML creates a connected line:\n
<visuals:PolyLineVisual3D Positions="-200 0 50, -150 0 0, -100 0 50, -50 0 0" LineThickness="15"/>
<visuals:MultiLineVisual3D Positions="0 0 50, 50 0 0, 50 0 0, 100 0 50, 100 0 50, 150 0 0" LineThickness="15"/>
The following rendering shows the difference in rendering the previous two lines in WPF 3D (left - PolyLineVisual3D creates a connected line; right - MultiLineVisual3D creates a disconnected line):