When you ruminate, it means you are thinking very deeply about something. You're likely to be so lost in thought that you stare off into space and don't hear people when they call your name.
Another meaning of ruminate is to "chew the cud," which can mean "to turn it over and over in your mind." Or, if you're a cow, to turn food over and over in your stomachs in order to digest it. Whether you're a human or a cow, if you ruminate, it will take a LONG time.