Twilio is a cloud telephony platform which can be used to create workflows and automate your calling and SMS related processes. It provides all kinds of APIs needed to build any telephony application.
When you sign up for Twilio, you get some free credits as well as a free trial period. Beyond that the features are pay per use.
Twilio's API can be used to automate your telephony operations like sending an SMS or sending an outbound call. All calls, recordings etc are accessible via the API and you can make arbitary behavior around it.