Twilio (twilio.com, on wikipedia) is the underlying service used by Switchboard to provide you with virtual phone numbers. Switchboard programmatically makes phone calls and sends text messages using Twilio’s API.
Twilio is a public company (TWLO) used by many well-known companies, like Netflix and Airbnb. Twilio offers email support during business hours in case you have any questions about Twilio billing.
Switchboard uses a feature within Twilio called Twilio Connect to manage on your behalf the virtual phone numbers you purchased with Twilio.