Just now, you have signed up for Mailgun. You have not given any credit card information. You have not verified a domain name, either. However, you have verified your Mailgun account. In this situation you face the issue Mailgun not sending emails.
Now, you are able to send emails only to the account with which you have signed up. But nothing is happening if you use any other email address. That is, you are unable to send emails to any other address.
Right now, you are stumped. You wish you knew why Mailgun is behaving in this weird way. You just want to send your emails to other addresses and not be stuck like this. You are looking for a solution to resolve your issue.
As per the Mailgun documentation, you should verify your domain so that you can send emails to other email addresses. Almost all the SMTP providers need you to do this action, which is essential to limit spam. Mailgun has been designed in such a way, and it also protects its reputation by making users verify the domains. Until you verify your domain, you will not be able to enjoy the full Mailgun functionality.
After you have verified your domain, you should be able to send your emails from that domain to all other email addresses.
Problem Mailgun not sending emails is solved.