ACOM is an abbreviation/acronym for Ancestry.com. All registered members to the site are able to send and receive messages through ACOM's message system.
There is a little green envelope icon (or should be) at the top right of your screen when you're logged into your account where you'll also find the hints icon and your username. It's next to a leaf, which is the icon for tree hints. The envelope will have a number if you have unread messages in your message inbox. You can click the icons to go directly to your messages or hints.