E-mails being sent by outside source

Although I have all my settings saying that my computer is safe and updates/scans run often, I had another instance where e-mails are being sent to certain people in my mailbox with a cryptic message and mysterious link.  It did show up in my mailbox as well with a "Norton-Spam Alert" heading, but it still went out to family and friends.  Why is this happening and what do I need to do to stop it from happening again?