It means more than one thing:
It can mean software similar to the link below, which is designed to allow you to circumvent common limits on e-mail attachments (often only 10 MB), allowing you to transfer large attachments.
http://download.cnet.com/Attachment-Manager/3000-2369_4-10908124.html
The other very common meaning to anyone, who uses Outlook is the Microsoft Attachment Manager, which controls what attachments are allowed based on settings since some are more dangerous than others.
Up through Outlook 2007 (does not work for 2010), I used to use this excellent program to control my attachments in Outlook:
http://www.slovaktech.com/attachmentoptions.htm
http://support.microsoft.com/kb/883260
It can even mean other things as in this link, although this is less standard a meaning:
https://addons.mozilla.org/en-us/thunderbird/addon/attachment-manager/