General Points
Species counterpoint is a method of learning how to compose simple counterpoint that was used by many of the great tonal composers. It encourages smooth, simple progressions in which there are few leaps and a variety of contrary and parallel motion.

Schenker suggests that these sort of progressions underpin well-written tonal music in the same way the 'Twinkle, Twinkle' underpinned the variation in the previous example.

One of the things that species counterpoint specifically forbids is parallel fifths and octaves (if you have ever had to harmonise a Bach chorale you will know all about these). Here are two parallel fifths followed by two parallel octaves. Schenker points out that composers generally avoid these sort of progressions, particularly in the two-voice counterpoint that he suggests underpins tonal music:

If you want to know more about species counterpoint it is discussed in detail in the Introduction to Species Counterpoint