The author has earned him/herself a Useless Use of cat (UUOC) award for not realizing that grep can take a filename argument in the example pipeline.
Basically, the example can be shortened to the following:
grep purple /usr/share/dict words | # Find words containing 'purple' in the system's dictionary
awk '{print length($1), $1}' | # Count the letters in each word
sort -n | # Sort lines ("${length} ${word}")
tail -n 1 | # Take the last line of the input
cut -d " " -f 2 | # Take the second part of each line
cowsay -f tux # Put the resulting word into Tux's mouth
Basically, the example can be shortened to the following: