Being difficult to understand and being downright insane, are very different things entirely, however this isn't always something that the average person will acknowledge or, even realize.
Sometimes straying from the norm, acting eccentric, openminded or simply giving up a little bit of one's strict logic, rules and sense of social guidelines for a minute smidgeon of insanity, can be a helpful thing.
An open mind, what some people fail to grasp, can sometimes be one's most important asset, allowing them to notice what other people might miss or write off as unimportant. Granted it would be quite an interesting and odd conclusion to say that grass isn't actually green, because of chlorophyl, but because it is clear and it's complex structure refracts light through it to appear green, it is something that a properly scientific and critical person, might need to consider if there happen to be few other explanations. Some people were thought of as insane for the hypotheses they suggested, but happened to be proven right later on.
It was considerations such as these that one Mr. Harry Potter, pondered over, when trying to make rational sense of the seemingly irrational Luna Lovegood.
He hadn't known her long, only met her a handful of times actually, but their meetings were reasonably pleasant, if a little confusing or, a better term might be baffling. She always came up with the most wild and mind numbingly complex explanations for things that clearly had a much simpler cause, like forgetfulness being caused by wrackspurts (small mites crawling around in one's head) or one's vision and other senses, apparently being controlled by zimphs (a helpful cousin of the wrackspurts, that told your brain what was going on). Harry briefly considered the effects that an extra five years lacking formal education, had on the average wizarding child's imagination.
If anything, he liked that she didn't seem to recognize he was a famous icon, or didn't put enough stock in the idea to act like most of the wizarding public did when in his presence. Even people at Hogwarts and within Harry's own house from day one, didn't always act entirely natural around him, talking to him as if he were of a higher station, or trying to make their achievements sound more significant compared to his "defeating Voldemort". In an attempt to be polite, or at least accepting, he would even attempt to debate her on her theories of the world around them, and while some of them sounded like something that should be in a children's storybook, like the ever popular and conniving gnargles that hid anything they could find, some things, like the idea that light was a weightless substance, that caused objects to shine, instead of shining itself, were thought provoking and interesting ideas.
She was more interested in muggle science than could first be grazed by talking to her, in fact she owned a number of high school science textbooks, previously used by her mother to concoct magical experiments. It turned out that her mother had often performed tests that juxtaposed magic with muggle scientific laws. The reason that one might not realize this at first glance is because, one, many people in the wizarding world were pure blooded and didn't own such books, much less take too much interest in them, and two, Luna had a tendency to take scientific laws, tear them apart, keep what she found useful, and attempt to produce countless other explanations.
Nonetheless, Harry was intrigued. For one, he was a normal person, to her, two, it was easier to talk to her about the muggle world than he could with most other people, save a few, including Hermione and sometimes Seamus, three, he found that he rather enjoyed exercising his imagination. It wasn't as if he'd been raised to think too much about childhood fantasies, for fear he get beaten as a result of voicing them.
He had experience with being an outsider as well, both in and out of the wizarding world, simply in different ways. He was either bullied and neglected or praised and overwhelmed. It would seem that Luna got the bad end of the stick, she was shunned by many a person in the only world she had ever known and simply, because she was a little bit out there. What one could realize while talking to her, is that her dreamy eyed, far away expression was simply a result of her often being lost in thought, and if one engaged her enough, it would slip away and she could, while significantly weird and nutty, be considered grounded to a point, when she wanted to be. She was clever, had a fairly smart sense of humour, if you could wrap your head her jokes, and she had nice platinum blonde hair, wait what?
Before he could continue his musings, he noticed his quill gain a mind of it's own and draw an arrow that pointed directly up his page. Following it up he stared into the stern face of his transfigurations teacher, Professor McGonagall.
"I trust you heard the last five minutes of my lecture on how one would go about the human transfiguration of scar tissue?"
she said in a calm, but accusing tone.
"Um..."
he stared at Hermione for help, but only received a glance and rolling of the eyes in return. After watching staring him down a moment longer she addressed rest of the class as a whole
"I expect a foot on the complications that arise in transfiguring various types of physical scars, and to those who didn't properly grasp today's material (she glanced pointedly at harry) it is described in greater detail in chapter seventeen of your textbooks. Class dismissed"
Harry gathered up his stuff and headed off with Ron and Hermione to lunch.