Species Counterpoint is that method of teaching laid out most famously by Johann Joseph Fux in his treatise Gradus ad Parnassum. Its method relies upon breaking contrapuntal study into five parts for each combination of two, three and four voices. The five parts (or "species") are as follows:
The first species is note-against-note counterpoint.
The second species is two notes against one in the cantus firmus.
The third species is four notes against one in the cantus firmus.
The fourth species is the study of suspensions against a cantus firmus.
The fifth species describes the combination of the four previous species together against a cantus firmus.
This is the simplest of possible contrapuntal compositions. It consists of one cantus firmus and one composed "counterpoint" to it.
Fux describes three-voice counterpoint as the most perfect because it is the only type in which it is possible to create complete harmonic triads without having to use an extra voice. That is, compositions which use more than three voices end up doubling triadic pitches, like the octave and the third. Put another way, three voice composition is the most perfect because it is the only way to express complete harmonic triads using a minimum of voices.
Four voice contrapuntal composition necessarily requires that, at least in harmonic triads, one of the voices be doubled. An exception arises in the creation of dissonant chords, like the dominant seventh chord.
Fux ends his book with the treatment of florid counterpoint (5th species) in four voices. Compositions which treat five or more voices are not much different than those treating four voices (and we know that treating four voices is not much different than treating three). Greater care must be taken in composing in more than four voices because as the texture becomes thicker, so it becomes more prone to error. All rules which apply to four voice writing also apply to all writing beyond four voices. If you write with more than four voices it might turn out strangely because you will have to double up a lot.