There are a few reasons why this could happen. Here's what happens...
As soon as you click on the 'Call' button, Exotel places a call from your Exotel number to your number. Once you pick up the call, Exotel calls the dialed number.
You may not get a call on your number if
1) Your number is switched off (doh!)
2) Your number is not reachable
3) There is an operator level connection problem (Eg: Calls from Tata to Vodafone are failing)
Ok. What can I do now?
Try calling your number from another number and check if the call goes through fine.
Call went through fine?
Raise a support ticket by sending an email to firstname.lastname@example.org with details like your username, the number you tried calling and the time of the call.