Apex Exception Email
Set the email addresses that receive notifications when your Apex code encounters unhandled exceptions. Emails can be sent to your Salesforce org’s users and to external email addresses.
Step 1 : Go to Setup
Step 2 : Enter Apex Exception
Step 3 : Select Apex Exception Email
Step 4 : Click Add Salesforce User Button
Step 5 : Select the user and Save
Step 6 : Enter the External Email Addresses
This Blog is very useful to learn about how to setup the Apex Exception Email in Salesforce.