E6 is built from E, G#, B and C#. E is the root, G# the major third, B the fifth and C# the sixth. Said aloud, its notes are E, G sharp, B and C sharp.
From the low string to the high one you hear E, B, E, G#, C# and E. Of the six strings you play, three give E, the note that names the chord. The lowest and highest notes are both E, two octaves apart, on strings 6 and 1.
E6 lets two strings ring open. String 6 gives E and string 1 gives E. Everything fits between frets 1 and 2. The second shape on this page starts at fret 9.
E is one change away. String 2 is left open, bringing in B, the fifth of E. E6 holds the whole C#m chord inside it, E, G# and C#. The change that keeps the most fingers still is to B7. One stays in place.
E6 shows up in six keys. In E major it is the I6, in A major the V6 and in B major the IV6. The rest appear in the key list.