The "speech" Sam gives at the end of the film (one of the few scenes written specifically for the movie) defines the trilogy’s heart. The Burden of Leadership:

Because The Two Towers is the middle chapter—traditionally the most difficult. It has no real beginning (the Fellowship is broken) and no real end (the Ring is not destroyed). The theatrical cut feels like two and a half hours of setup for The Return of the King . The Extended Cut, however, breathes. It allows the sadness of Boromir’s death to linger, the stubbornness of the Ents to frustrate, and the heroism of a second son (Faramir) to finally shine.

Beyond the Hornburg: Why the Extended Edition of The Two Towers is Essential The Lord of the Rings: The Two Towers

We witness the actual burial of Théoden's son. This scene features Éowyn singing a haunting lament in Old English (Rohirric). It highlights the heavy toll of Saruman's raiding and establishes why Théoden feels so defeated and protective of his people. Aragorn and Brego: