The answer has only come to me recently, through lots of studying and pondering and talking to people smarter than me (they're not too hard to find). The simple answer is, a spell is a different kind of prayer.
Yeah, yeah, I know, that doesn't make a whole lot of sense. Aren't you glad I'm not just leaving you with the simple answer? At any rate, let me clarify. In a standard prayer, the communication is one-way. "God, please let X happen". Your ability to do anything doesn't change; the diety gets to do all the work If It So Pleases Him/Her.
When looking at the Wiccan-Ritual-As-A-Prayer model, there are several areas of difference. Primarily, those differences are communication, ability, and working.
In a Wiccan Ritual, communication is two-way. You start the conversation, and the Divine joins in. It can be verbal, or, more often, a feeling of connected-ness, a feeling of give-and-take going on just beyond the edges of your perception. There are a myriad of other forms this commucation can take, but if it's not two-way, you may as well just stop now because for some reason or another, the Divine isn't paying attention to you. The communication is essential. A prayer is mailing a letter. A ritual two modems making beepy noises at each other.
In a standard prayer, there's no change in ability on the part of the pray-er. You're sending a problem off to someone more able to handle it than you are.
In a ritual, you are (ideally) connected to the Divine. That's what all the modem-beepy-noises were about: making a connection. Integrating your energy seemlessly into the energy that makes the world work, making you a part of something that much larger than yourself.
The Divine has granted you access to its resources, to give you the ability to make change that you didn't have before with just your own personal energy. Of course, with this ability comes doing the actual work. YOU have to choose what energy to use, how to mold it, how to shape it, how to direct it, and how to let it go. What has happened here is the Divine has given you the ability to fix the problem yourself, but you still have to do the work.
And perhaps more importantly, you have all the responsibility. There's no passing-the-buck, satan-made-me-do-it, it's-not-my-fault nonsense here. Anything you do, you did . It's your responsibility to do it right, and to do it ethically. The Divine entrusted you with a hammer, but if you beat someone over the head with it, it's your fault.
Anyway. With all that out of the way, let's get back to the props.
The props help in all three aspects of the ritual that differ from prayer. This is because most of the communication and work is done on a sub-concious level. Your waking self would have a hard time interfacing with something that amazingly huge without imploding. The communication is mostly outside your immediate senses because your subconcious is handling it. The symbols, the props, the correspondances, all of these help you keep your focus. The things we use have been used so much for similar purposes that our subconcious automatically generates a meaning to them all. We, awake, are working with props that all symbolize something, and in turn our subconcious is working with the energy represented by our props to achieve the result we're looking for. The symbols are our wakingness interfacing with our sub-concious.
That's why people who are really good at it don't need any tools at all; they have that much control over parts of their mind other than their waking conciousness. It AIN'T easy. Beginners can do it too, but they have to work harder and their results are generally not as effective because of a lack of focus. Not everyone is born with the ability to force their "lower self" to focus on a particular task at hand.
And that's why we use props. Feel free to tell me how wrong I am, if you have a different belief on the matter. My e-mail address is firstname.lastname@example.org . I always welcome differing theories.