As I understand this sketch (it is not completely accurate and there appear to be some half drawn elements):
A is the pivot point of the arm
E is the fixed end of the pneumatic cylinder
(A and E are both attached to the same structural element and do not move relative to each other)
D is the other end of the cylinder when the cylinder is retracted (I believe the smaller circle should have been drawn with the distance from E to D as the radius of the circle rather than the diameter of the circle)
C is the other end of the cylinder when the cylinder is extended (same problem with the larger circle)
Therefore the line segment AD is the arm position when the cylinder is retracted and AC is the arm position when the cylinder is extended (thus the “X” motion off to the right hand side of the sketch).
It is not clear what the sketcher was attempting to draw with the lines originating at B. Perhaps the sketcher was attempting to show what happens when you shorten the length of the arm between the arm pivot and the cylinder attachment point. This part is not very clear and does not appear to be drawn correctly (BC is shorter than BD and since the two circles were drawn incorrectly, it made it hard to use those two circles to illustrate the point he was trying to make).
Anyway, I might be wrong with my interpretation of this drawing.
Basically, since the cylinder is pivotably attached at each end, the locus of points that define one end of the cylinder relative to the other is a circle around the fixed end. There are two circles, one for the retracted cylinder and one for the extended cylinder. The arm is a line of fixed length between the pivot of the arm and where it attaches to the cylinder. Since the pivot point of the arm is fixed, you can draw a circle around that fixed pivot point whose radius is the length of that arm. Where that circle defining the length of the arm intersects with the two circles for the cylinder lengths are the two positions of the arm. At least that is how i usually sketch this problem.