The way that Witches and Wizards think about everything, including spells, is completely different from the way we Muggles think about it. When we consider the mechanics of, say, aiming a spell at something, we ask "muggle" questions like "Do you have to have line of sight?" that they would never think to ask. We are used to Muggle physics and Muggle limitations. Witches and Wizards are used to Wizard physics and Wizard limitations. That makes all the difference in the world. In fact, it is literally a different world.

A great example of this is Molly Weasley's reaction to the fact that the Anglia fits so much inside its trunk and can seat five people across the back seat comfortably. It doesn't strike her as the least bit odd, since she thinks with Wizard logic. It is so completely normal to her that she even assumes that the Muggles made it that way; she doesn't realize that it's unique to the Wizarding world. But we, as Muggles, would be unable to comprehend how such a thing could be. Our world and life view, our structure for how things work, is so utterly different from the way Witches and Wizards see it that we have a difficult time understanding the way magic works. Molly, on the other hand, can't understand our notion of three-dimensional space and physics, which is based on science and technology. A car that couldn't hold more when necessary would make her do a double-take. Remember Ron poking Dean Thomas's poster of West Ham United, trying to make it move? It just didn't make sense to him.

Consider that the physical laws that govern our world--cause and effect, action and reaction, conservation of energy, that sort of thing--are secondary in the Wizard way of seeing things. For them, the key is intention and power. Does Molly have to see something to Accio it, or even know exactly what that thing is? Nope. She has the intention and power to make that Accio spell do exactly what she wants. Harry, as he's learning it, needs to specify, even see the object in question. But by the time he's summoning the Triwizard Cup in the graveyard, he has all the intention and power he needs, almost without realizing it, to make exactly what he wants come directly to him. No specific target needs to be stated because of the desperate focus of his own mind.

Once we free our mind of the shackles of Muggle physics, magic becomes that in a way more understandable, and it soon becomes obvious that magic is really the manipulation of magical power by the intention and focus (by means of a wand and words, usually) of the caster. The exact physics of the spell--how it works, how it's cast, what it does--can be different every time, because physical laws aren't involved, emotions and intentions are.

That means that a spell could have a markedly different effect depending on the cirsumstances of it's casting (such as Expelliarmus actually throwing Lockhart against the wall, since Snape's intentions caused a somewhat more violent result). It also means that Hermione can create a spell on the spot (Mobiliarbus, which literally suggests moving a tree...you can't tell me that third year Hogwarts students have learned spells to move trees...she made it up on the spot, using her intention and her understanding of the language of spellwork) [1]. In it's purest form, magic requires no words and even no wand. We see Dumbledore using magic this way, or close to it, almost every time he 
does it.

There are three properties to a spell, and physical laws aren't involved at all. The three are intention, focus of power, and focus of mind. The intention comes first, obviously, since the spell caster needs to intend to do something. Then the spell words are used to focus the mind on the action desired, sometimes with the assistance of a specific thought pattern. These two are intertwined, since the words often marshall the mental processes, but sometimes a certain type of thought is required first, such as the happy thought to trigger a defense against Dementors. Then the wand is waved in a specific pattern to focus and direct the magical power of the caster's body toward the goal. All of these things work together to create an effect which simply does not obey any of our Muggle scientific laws. But the key to the whole thing is intention. [2]

If we think like Muggles, this is truly, utterly, unbelievably amazing. That's part of what makes the books so much fun. But if we could truly think like Wizards, it would be completely normal, even mundane. And for kicks, you would read comics about Martin Miggs, the Mad Muggle.
 

NOTES
[1]  Hermione may have a number of arcane spells memorized--Alohomora comes to mind--but I still don't believe that she learned a spell that moves a tree. That isn't even a logical spell to have. What makes a lot more sense is that she understands the root words and has no problem creating the words she needs at the time she needs them. After all, to move Snape in PA they used "mobilicorpus," which is basically the same spell with a different thing being moved ("corpus" in Latin means "body" while "arbus" refers to a tree). Hermione, being as bright as she is, has quickly moved past simply parroting back spell words and has grasped the underlying logic to the whole thing. She doesn't know a specific spell to move a tree, but when she needs to move one, she knows how to create the correct incantation. Alohomora, on the other hand, is a very obscure spell. The etymology is definitely not simple Latin like so many of the others. It is specifically refered to as "her" spell. It seems fairly obvious that Alohomora is one she dug up in some dusty book somewhere in the library, doing a bit of light reading. And when she spotted it, of course she'd see the usefulness of it and memorize it. But Mobiliarbus? You think she saw that and said to herself, "Well, you never know when I might have to move a tree!"? No, that's a spell of her one invention, improvised on the spot using her understanding of the way magic works. That's completely logical and actually show just how advanced she is, if you think about it. Its a good example of the working of the mind of someone who gets over a hundred percent on a Charms exam.

[2]  One more note on spell words and intentions: think about Wingardium Leviosa. The meaning of that spell refers to levitating a feather (the root word "wing" in there is clearly not Latin, which has no letter 'w', but refers to the object they were supposed to be lifting). But later on, Ron, who doesn't really get it yet, uses those words to levitate a troll's club! How can this be? Because his intention came into play, and his mind was totally focused on what he wanted to do. The words he said were what he THOUGHT would levitate anything, since he doesn't really understand what the phrase meant, and sure enough, it does. Since he believed that those words would have that effect, they sufficed to focus his thoughts. Hermione, by the time she is in her third year, would have used "Clava Leviosa" instead, whether or not anyone had taught her that specific incantation. If she didn't know the Latin word for "club" off the top of her head, she would have just said "leviosa" and concentrated on the club.