Twilio Functions is a serverless environment that allows developers to build and run Twilio applications using Node.js code. It provides benefits such as security, no infrastructure requirements, auto-scaling, and native integration with the Twilio REST Helper Library. The Phone Verification API is used for fraud prevention and transaction verification, allowing users to verify phone numbers and codes sent via SMS or voice calls. To get started with Twilio Functions, developers can create a new function and use the JSON Response template. The code provided demonstrates how to start and check the verification of a phone number using the Phone Verification API. The process involves sending an HTTP request with the required parameters and verifying the response from the Phone Verification API.