Common Fingers (also known as Pivot Fingers) allow you to keep one or more fingers in place while changing chords.  While most self-taught guitarists remove every finger while changing chords, using common fingers saves two movements ( the clearing and the returning to the same place) and increases accuracy.


Example 1

Notice the position of the third finger in each chord.  It is on the same string and in the same fret. 
This is a common finger.


Example 2

It is also possible to have more than one common finger. 
Note that the first and second fingers are common to both the Am and C.


Example 3A

Common Fingers can also be created.  In this example, the two chords seem to have no fingers in common.


Example 3B

But if we re-finger the Em with 1 and 2, we can create a common finger between the chords. 
Now the first finger is common to both chords.