Next.js Middleware allows modification of responses based on a user's incoming request or location, enabling features like localization, personalization, authentication, and A/B testing. On Netlify, Next.js Middleware can run at the edge, improving performance and reducing latency, and can also be used with static pages or Incremental Static Regeneration (ISR) to add dynamic magic to prerendered pages. Edge Functions offer more flexibility and power in transforming responses, allowing developers to process responses chunk by chunk without waiting for them to fully load, resulting in less latency and better memory usage.