Chain emails are those that, in the body or subject of the message, asks the recipient to forward the email on to multiple people. Many chain letter emails are hoaxes and are often considered to be a security and privacy risk.
Chain emails are often used to collect valid lists of email addresses. If the message is forwarded on by a person, it will usually show the names and email addresses of everyone they have sent it to, and possibly the addresses of everyone the last person (from which you received it) also sent it to.
The risk is that you do not know if an unscrupulous or malicious person will receive the email with all the addresses, and what they might choose to do with that list. Many consider chain email to be a type of spam.