Neon's serverless driver allows for the use of Postgres at the Edge with Vercel Edge Functions, providing a convenient solution for applications that require database operations in edge environments. The driver separates compute and storage, making it suitable for use with Next.js API Routes. It offers flexibility in querying using SQL-over-HTTP or WebSockets, depending on the application's needs. With Neon, developers can utilize Vercel Edge Functions to read and write data, enabling efficient and scalable database operations at the edge of the network.