Factual error: The film takes place in a private boarding school the 1950's, however one of the students is studying from a 1980's chemistry textbook. The obvious giveaway is that the spine of one book shows HBJ as the publisher. Jovanovich was not added to Harcourt Brace until the 1970s.
Factual error: Keating misquotes Whitman's "Song of Myself". The word "rooftops" should have been "roofs". An English Lit teacher of his caliber would not have made this mistake. This is a deliberate mistake on the part of the filmmakers.
Chosen answer: It is a classroom exercise. He is being followed by pupils and is reinforcing their latin vocabulary by taking them on a tour of the garden and showing them the things that the words actually relate to (edificium = building, flora = flower etc.) This contrasts with his earlier behaviour when he simply had them mindlessly recite conjugations (amamo, amamas, amabat). The point is that this illustrates how the Latin Master has been affected by his contact with Keating and has become a better teacher as a result.
Oscar Bravo