Twilio's REST API is the way in which you'll proactively interact with your Twilio account. This contrasts with TwiML, which is used to shape the flow of individual calls and incoming SMSes.

It programmatically gives you access to all of the data and features accessible from your Twilio dashboard, ranging from logs of previous calls to records of phone numbers you've purchased and is used to trigger outbound calls and SMS messages.

RESTful APIs are centered around data. Effectively, the API models various kinds of resources that Twilio holds, such as calls, phone numbers, or messages, and lets you perform Create, Read, Update, Delete (CRUD) operations on them.

If you're not familiar with REST APIs and how they work, IBM has a helpful primer at http://www.ibm.com/developerworks/library/ws-restful/.