The extend tool is designed to allow connecting line segments that do not intersect or share vertices. The nearest end point of the line will be extended with an additional line segment to reach the closest part of the 'Extend-To' line that was first selected.
Line extension is a two step process:
Select Feature to Extend Lines to
With the Digitizer tool, select the line feature you would like to extend one or more line features to. Then from the Move/ Reshape Features right-click or Digitizer menu, choose Select Feature to Extend Line To.
This sets the master line that any subsequent lines will be connected to.
Extend Selected Lines
Next use the Digitizer tool to select the line feature to be extended. From the Digitizer menu select Extend the Selected Line(s) to Extend - To Feature from the Move/ Reshape Features right-click menu option.
This line will get an additional segment added to the end of the line to reach the closest point on the line previously set.
To just extend a line feature, not in relation to another feature, use the Insert New Vertex tool.