You can decide whether or not people can see when your online and when you were last online.
To change this setting, navigate to your profile and select Edit fun stuff about me
Scroll down on the edit page and you will see two settings, Show when I am online and Show when I was last online. If you check these two settings, then other users will be able to see when you are online and when you were last online. If you uncheck them, then other users will not be able to see this
