Be sure to scroll down... there may be more than one question on this page!
The simple answer is to stand in the doorway with your back against the hinges. If the doorknob is to your left, it is a left-hand door. If the doorknob is on your right, it is a right-hand door.
Now, in the case of exterior doors (which typically open inward), you must designate that the door is a left-hand inswing or right-hand inswing. The designation "inswing" not important for interior doors because both sides are finished the same, But for exterior doors, it lets the manufacturer/supplier know which side of the door is the outside, which is often clad or finished differently from the inside.
The problem is in their description of "handing". If you look at the diagram on their website, they are labeling the "handing" based on the lockset orientation you need to choose, not using the typical industry standard for handing.
What they call "left-hand outswing" is (in the door industry) actually "right-hand outswing". The left hand inswing and outswing (per their diagrams) use the exact same lockset (with the key on the outside). In other words, the lockset handles look the same but the latch plate is rotated 180 degrees so it latches properly.
I guess they changed the standard handing conventions to make is easier for the customer who doesn't know anything about handing to order. Otherwise, they would have to call each lock both left and right handed, adding to the confusion. Based on the description of your door, it is indeed a left-hand outswing, but for ordering purposes from this company, indicating "right hand" in the order follows their modified convention.