The intent of this semi-famous sentence is that the horse was what fell, after it was raced past the barn...
From the "Garden path sentence" entry in Wikipedia:
This sentence relies on the ambiguity in English between the passive participle and past tense. Since raced is usually encountered as an active verb, the initial parsing of this sentence is the horse (noun phrase and subject) raced (active past-tense verb) past the barn (prepositional phrase), but this parsing cannot make sense of the word fell at the end of the sentence. The proper parsing is The horse (noun phrase) raced past the barn (participle phrase) fell (verb). More explicitly this sentence can be written as The horse that was raced past the barn fell, where that was raced past the barn tells the reader which horse is under discussion.