How do I stop my iMessages appearing on my MacBook Air?
The best practice would be to have other users set up with their own logins on your Mac or to use the Guest account.  They would never see your messages in that case.

But, if you really wish to disable iMessages from appearing on your Mac:


Go to Messages
Open the Preferences Messages > Preferences or ⌘+,
Go to the Accounts tab
In the iMessage account uncheck "Enable this account"