A red-eye flight is a flight that takes place during the middle of the night. For them to work there needs to be a change of time zones by at least two to three hours or be a very long flight. As far as I've seen it is only possible for them to work flying west to east (lax-ord), or south to north (gru-ewr). Either way these flights usually depart at 11pm to 1am local and arrive at 5:30am to 7am local. And just like the name implies when the passengers arrive at their destination after an all nighter that is exactly what there eyes look like!
For the flight the post was about it is going to leave ONT
at around 12:40am, and arrive IAH
at arround 6am. Business men seem to like these flights because it gives them the ability to arrive at the beginning of the business day.