Well after your chats are complete you need to logout from Whatsapp Web so that others won’t see your messages if the computer is a shared one.
Simply click the menu and choose ‘Logout’.
If you are using multiple browsers then you can disable access from your WhatsApp account at once by going to ‘Menu>Whatsapp Web’ in the Whatsapp app. Here you will see all the list of browsers from you are currently logged in. Tap ‘Log out from all computers’ and you are done.
Don’t know how to set up WhatsApp for web click here