Peter Jackson's best change to Lord Of The Rings: The Fellowship Of The Ring was how the portraly of Boromir's death, the movie's most meaningful scene. To make The Fellowship Of The Ring work as a movie, changes to the original Lord Of The Rings books were inevitable. The novel is too long to include all of J. R. R. Tolkien's original story. With the sequels, The Two Towers and The Return Of The King, in mind, Peter Jackson was right to condense Boromir's arc into the first movie.
Played by Sean Bean, Boromir is a member of the group that volunteers to help Frodo destroy the One Ring in Mount Doom. He is a famous warrior who joined the fellowship to protect his home, Gondor, from the evil of Sauron. Unlike the others, Boromir believed that the Ring could be used to defeat Sauron. That belief corrupted the noble Boromir to the point he tried to forcefully take the Ring from Frodo, but the Hobbit used the Ring's power to get away. His death shortly followed when he was shot down by orcs while looking for Frodo, marking another on-screen death for Sean Bean.
Boromir's death is one of the most memorable moments in The Fellowship Of The Ring, but it wouldn't have happened when it did if Peter Jackson had faithfully followed the books. In Tolkien's series, Boromir is still alive at the end of The Fellowship of The Ring and isn't killed until the beginning of The Two Towers. Although the events of his death in the movie are similar to the book, Boromir's demise is shown in full in The Fellowship Of The Ring, rather than being split across the first two installments. The decision neatly wraps up Boromir's story and gives the movie an exciting, but emotional endpoint, rather than the anti-climatic cliffhanger from the books.
Boromir's movie death sets the direction for the rest of the fellowship in The Lord Of The Rings movies, most notably Aragorn, in a way the books didn't. Part of the reason The Fellowship Of The Ring is considered the best Lord Of The Rings film is the tension between Boromir and Aragorn, built up because both have a claim to be the king of Gondor. With Aragorn a threat to the throne, Boromir is naturally skeptical about him. But on his deathbed, the proud and stubborn Boromir finally shows his acceptance of Aragorn as the future king with the iconic line "I would have followed you my brother, my captain, my king." In the book, he doesn't give Aragorn the same approval. Instead, his dying words are "Farewell, Aragorn! Go to Minas Tirith and save my people! I have failed." By calling the people of Minas Tirith, the capital of Gondor, his people, Boromir in the books proves that he still sees Aragorn as an outsider, rather than a brother.
Boromir's death also marked the breaking of the fellowship, which allowed Peter Jackson to frame The Two Towers around the different groups. Frodo and Sam continue their walk from The Shire to Mordor, while Aragorn, Legolas, and Gimli go to Rohan, and Merry and Pippin are hostages of the orcs. Boromir's fall acted as a catalyst for these storylines to break off, so it made sense for The Two Towers to pick up from that point. The change from the books also meant that instead of Boromir's death, the second movie opened with the memorable fight between Gandalf and the Balrog. By bringing forward Boromir's book death and changing his relationship with Aragorn, Peter Jackson created one of the best The Fellowship Of The Ring scenes and perfectly set up the rest of the series.