Night terrors are when a person seems to wake from sleep, absolutely terrified; but when, in fact, the person isn't awake and only appears to be (sort of). Night terrors are different from nightmares, which can be terrifying but are a different thing from night terrors.
When children have night terrors they may outgrow them. My son had them, and he outgrew them a little at a time (they got less and less severe as he got past being a baby and lower grade-school-aged child.
When a child has night terrors his state of terror is obvious, but since he's not really awake there really isn't any talking him out of them. It's as he seems to "come out of them" (wake up a little at a time) that he calms down. He may go on to wake up all the way, or else he may never really seem to wake up completely and just go back to sleep. Night terrors are more likely to happen at a certain stage in sleep, and they're more likely to happen if the child/person has had a lot of stress (but in the case of a child, that "stress" can be as benign as a very happy and busy day in which there hasn't been much chance to spend a lot of time being calm).
This is NOT a scientific explanation for the cause of night terrors, but my personal theory about my son's experience with them is that there is at least the chance a stay in a hospital when he was an infant could have had some impact (maybe even terrorized him) when he was too young to remember it. I couldn't help but wonder if that feeling (that he didn't recall and couldn't process the way someone older could) may have returned when he'd reach that certain stage in sleep if I let him go to bed too early. If I didn't let him go to bed too early he wouldn't have a night terror. It always seemed as if when he was sufficiently tired out before sleeping he may have gotten past whatever "stage" it was that resulted in night terrors. As he got to be school aged, his terrors decreased in severity until they first turned into "mild confusion and anxiety" and eventually resulted in a few "spaced out sleep-walking" incidents.