I always assumed it was a sign that an otherwise unassuming and placid teacher had a ruthless streak and could deal swiftly and, if necessary, brutally with a situation.
---The book explains it (and it was written pre-Harry Potter). The owl had been nesting in the disused chimney. When Prideaux fired it up a half-dead owl was smoked out onto the classroom floor, shocking and startling the boys. Prideaux whisks it up and out of the room. Later the boys find the dead owl on the rubbish heap, its neck neatly twisted and broken. The point is that Prideaux is a skilled killer. Also in the book, Haydon is killed by persons unknown, his neck neatly twisted and broken.
The movie version compresses the more nuanced details from the book (that also foreshadow the different details of Haydon's death). But the essence that Prideaux is a capable and ruthless killer when required are preserved in a simpler, shorter scene.