SMS can also be received and processed automatically. This enables services such as delivering information on request (for instance, send INFO GOALS to receive the results from the Soccer League), but also more complex flows such as in bots, which can have simple conversations with users that enable rich services such as remotely configuring a thermostat.
Each time Twilio receives an SMS to one of your registered phone numbers, it performs a request to a publicly available URL. This is configured in the service, meaning it should be under your control. This creates the problem of having a URL under your control available on the internet. This means that just your local computer won't work, as it's not addressable. We will use Heroku (http://heroku.com) to deliver an available service, but there are other alternatives. The Twilio documentation has examples...