Why does the development section often move through several keys?

In the context of sonata form, the development section serves as an area of tonal flux designed to resolve the conflicts of tonality and theme established in the exposition.1

The section moves through several keys—often involving a rapid series of modulations—for the following reasons:

• Dramatic Contrast: By creating a state of harmonic instability through frequent key changes, the composer casts the eventual return to the tonic key in a much stronger, more dramatic light.2
• Thematic Exploration: The development section breaks down principal themes into smaller elements, placing them into new tonal or contrapuntal relations. Moving through different keys allows these fragments to be heard in new contexts, demonstrating their hidden importance or expanding the scope of the movement.1
• Resolution of Tension: The tonal system relies on the interplay of tension and resolution. Modulation away from the tonic creates tension, which is then resolved when the music returns to the home key. The development section utilizes this instability to build toward an expressive climax before the final resolution.324