Michael Peacock discusses using Twilio and PHP to build telephony applications. Twilio allows developers to make phone calls, send SMS messages, and other telephony features through simple HTTP requests. Applications are controlled through XML responses which dictate what Twilio should say or do. PHP has a library that simplifies interacting with the Twilio API. Basic applications can be built in minutes to provide phone menus, gather input, and process responses. Twilio provides tools for debugging applications and offers services like phone numbers and hosting.