This is a fairly broad problem and could be the result of several factors. Please go through the list below and eliminate each possible problem:
Guideline 1:
Make sure you have your outgoing SMTP Mail Server set to mail.yourdomain.com.
Guideline 2:
Make sure you have a connection to the Internet when trying to send outgoing mail.
Guideline 3:
Make sure your domain name is using right name servers.
Guideline 4:
Make sure you have authentication enabled for outgoing email.
Guideline 5:
Make sure that all recipients have valid e-mail addresses.
Guideline 6:
Make sure you are using the FULL email address as your username.
Remarks !
If all of the requirements above are met, there should be no other reasons why you cannot possibly send outgoing e-mail through your SMTP server. The most common problem is that a client will forget that they must set their email client to authenticate before they can send their outgoing e-mail.
Remarks !
Additionally, new clients usually have this problem while their domain name is in the process of being propagated, in which case they must simply wait for propagation to take place.