What is Neil Armstrong teaching in this image?
1)  The triangle shape represents an aircraft-- imagine something like a supersonic version of a Gee Bee racer.  The thing at the leading edge of the vertical fin is the canopy.

2) Here is a sketch that offers an educated guess about parts of the diagram that are either cropped, or hidden behind Neil Armstrong, in the original photos.  Also, for added clarity, labels have been added to the dashed lines representing the horizon, and the aircraft's longitudinal axis.  Note that for the diagram to make sense, the wings must be attached with zero incidence relative to the longitudinal axis of the vehicle, or the vehicle may be a flat-bottomed wingless lifting body.   Only the green vectors represent actual forces.  "L" is the lift vector, "D" is the drag vector, "W" is the weight vector, and "T" is the thrust vector.  Note that "D" is parallel to the flight path, "L" is perpendicular to the flight path, and "W" is perpendicular to the horizon. "T" is drawn in this sketch as nearly, but not quite, parallel to the aircraft's longitudinal axis-- in the original, the direction of the "T" vector is about midway between the direction of the aircraft's longitudinal axis and the direction of the flight path.  No attempt has been made in this quick sketch to make the force vectors add to zero.  We can't see enough of the original to guess whether the force vectors as drawn there would add up to approximately zero or not.  

3) The vector labeled "flight path" in this sketch was labeled "V" (for "velocity") in the original.  It represents the aircraft's instantaneous direction (and speed) of travel through the airmass.

4) In the original, the line representing the orientation of the longitudinal axis of the aircraft was simply an extension of the flat bottom of the aircraft; it ended up getting displaced upward a bit in this sketch. This wasn't intentional but does have the effect of causing the line to pass closer to where the aircraft's CG would likely be. The angles of interest can be represented accurately regardless of whether or not the line representing the orientation of the aircraft's longitudinal axis actually passes through the CG or not-- we just need a reference line that is parallel to the aircraft's longitudinal axis.

5) Another detail that ended up different from the original in this quick sketch is the order of the angles illustrated on the left-hand side of the diagram.  In the original, running from right to left, the order is gamma, alpha (this letter has been rotated about 45 degrees clockwise so it looks almost like an upside-down gamma), theta, while the order in the attached sketch is theta, gamma, alpha.  This has no effect on the meaning of the diagram-- the same greek letters are still associated with the same illustrated angles. A confusing point about the upper photo is that it is cropped in such a way that at first glance the angle labeled "theta" appears to duplicate the angle labeled "gamma", but of course this is not actually the case.

6) It appears that the curved line represents the surface of the earth, the overlined "R" represents the radius of the earth, and "h" represents the aircraft's height above the earth's surface.  Neil is probably explaining that at very high speed, orbital effects start to come into play, reducing the need for lift.