How does binary form organize two related musical sections?

Binary form is a structural pattern in music characterized by two complementary, related sections of roughly equal duration, often represented as ab.1

The organization of these sections relies on a specific harmonic journey:

• First Section: The piece begins in the home key (tonic) and modulates to a new key, typically the dominant (the fifth degree above the tonic). For compositions in minor keys, the modulation is usually to the relative major.12
• Second Section: This section begins in the new key. It explores various harmonic movements before returning to the original home key.12

While these sections are not required to be monothematic, they generally rely on closely linked melodic and rhythmic materials. In many 18th-century compositions, these sections are separated by double bars with repeat signs, creating an aabb structure. Some works utilize "rounded" binary form, where the second section returns to the melodic and rhythmic features of the first section, bridging the gap toward ternary structures.1