Yahoo! Messenger is intended to allow you to engage in private conversations.
However, this doesn’t guarantee that your conversation will never be available to others. As with any conversation, the person you correspond with might share the content of your conversation with others, or an outside party might intercept the conversation as it crosses the Internet.
If your organization uses a firewall, your administrator might have the ability to review any of your network traffic and content, including any instant messages you send. If you’re concerned about this, you should discuss this with the organization giving you Internet access.