A stemming algorithm lets you reduce each English input word to its basic root or stem (e.g. 'walking' to 'walk') so that variations on a word ('walks', 'walked', 'walking') are considered equivalent when searching. This stems can than be used in a search query rather than the original words, which generally (but not always) results in more relevant search results.
His code example uses the library to search for two different types of strings - a single word and a phrase (with stop words removed). The Stem() method is called on the word and the results are looped through to remove all matching the values in the stop words array.