The Address API by Twilio allows developers to easily provide addresses for their business applications, enabling the purchase of local phone numbers in countries with address requirements. The API provides a simple way to manage addresses and satisfy country-specific address requirements. A .NET MVC application demonstrates how to use the Address API to create an address management system that allows users to add, view, update, and delete addresses. The application also includes a search feature for available phone numbers in countries with address requirements. By using the Twilio Addresses API, businesses can provide a first-class experience to customers worldwide while meeting country-specific regulations.