Order not completed in the backend list. What is means?

Order not completed in the backend list. What is means?

Hi to all..
I can place an order without any error messages from the front-end. I select the product, select the payment method and confirm the order.
In the backend I find the order with the status "not completed".. what is means?

If i deselect the voice "payment" in the "function of the shop" and I try to complete a new order I see the order with the status "completed"..
So I think that the problem is the payment but I don't understand the cause..
Someone can help me..

Thank you

Aw: Order not completed in the backend list. What is means?

Someone can help me?

Thank you
simone