Incomplete order status is assigned for the orders where customers start checkout process but never complete. You can see this orders in admin to analyze customers behavior or catch some issue with checkout. Other statuses are more related to the demo data. Say you can set up some of your payment method to set Failed status in case of payment declined by bank. Take a note you can add your own statuses or rename current.
Make sure you have write permission to resources/cache and other important folders. You can enable System check (System > Settings > System) and it will report you problems after some time