Twilio and Node.js are used to send vCards, which are electronic contact cards in a standardized file format known as VCF, to customers' phones. This allows customers to easily import business information into their contact book. To set up the application, a new Node.js project is created and dependencies are installed, including Twilio and vcards-js packages. A .vcf file is stored on a local server using ngrok to expose it through a public URL. The vCard properties are populated with customer data, and then sent as an MMS using Twilio's MediaUrl parameter.