Stealth mode is used to mask your online status while chatting. Activating stealth mode will inform other users that you have gone "offline" and prevent their messenger from displaying you as online. In Adium, stealth mode is called Invisible (mainly for consistency with AIM, which had it first and calls it Invisible).

Activating stealth mode

Choose Invisible from the Status menu.

Alternate Method

Choose Invisible from the Status Bubble located in the header of the Contact List.

Stealth mode may also be activated on individual accounts in the Status menu.