Skype is an instant messaging program that allows you to communicate to other contacts via either a webcam or standard instant messaging. The program also allows you to change your status from online to busy, away or invisible. While invisible, a user appears to be offline to all other users on his/her contact list. This prevents unwanted messages. As of October 2010, no programs exist that tell you whether someone is or isn't online, but there is a small trick you can do to figure it out.
Open a conversation window with the contact you believe may be invisible.
Send a message to that contact. If the contact is offline, you will receive a message from Skype saying that "The contact is offline, your message will be delivered to them when they sign in." If the contact is online but using the invisible status, you will not see this message.