theories of arcana 101

Material components and magical items both have a similar reasoning, in fact: the Law of Similarity, which says that like is connected to like. This is one of the fundamental psychological principles underlying practices of magic in the real world. A magician sprinkles water on the forehead of a baby because this is similar to the process of spiritual cleansing that he intends. (Material component.) He manipulates a mannikin in the shape of a person, bound around with wire, because he intends to hinder that person. (Focus component.) He touches his body at points in the shape of a cross, because the cross is symbolic of his lord's authority, especially to the symbol-affected demon he seeks to exorcise. (Somatic component.)

The Laws of Similarity, Sympathy, and Contagion all have to do with symbolic connections, and form the basis of most real-world magical traditions, whether mystico-religious or wholly constructed -- and to believers, the difference is usually nil. Historically, one religion's blasphemous sorcery, was for the most part another religion's... religion. Voodoun is engages in all manner of spells and rites, but is an honest religion to its practitioners. Perfectly devout Christians shell out major bucks for bottles of holy water or seek magical healing at the end of a pilgrimage. A Shinto ofuda is a basic sort of amulet, a magical device, but it's also religious paraphernalia, a holy symbol. In RL cultures, magic is religion, and vice versa. Just to give one example relevant to D&D, a "ghost shirt" is a common magical item made by various cultures who had to deal with guns -- the name come from the Lakota version. You could call them a casting of Protection from Arrows, or magic armor with the Arrow Deflection ability. To the Lakota, they were made through divine power.

Not that they worked... but that's divinity in the real world for you.

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A version of this line of thought causes me to comment on your mention of sacrifices. This is indeed a particularly powerful notion; typically, the sacrifice is either propitiatory ("bad spirit, please take this little bit and be satisfied instead of tormenting us") or placatory ("sorry I sinned, here, please this as a token of my apology"), or in offering ("I've got something here for you, I'll remove it from the material world and send it to the spirit world for you to have, now could you please do me a favor?"). (Socially, a big sacrifice also told all the other humans around that the sacrificer is really sodding rich. A hecatomb is a hundred head of cattle. That's nothing to sneeze at, even today, and back in Greek days it was a fortune.) The notion of sacrifice as the basis for a religion always struck me as a useful understanding of Erythnul, an otherwise fairly nonsensical sort of deity. The concept is also easily transferrable to any other evil deity, with sacrifices ranging from personal scourging of the flesh to good old-fashioned blood-on-the-altar human sacrifices. Followers would understand sacrifice as the holy medium of communication between man and god.

Another example to add here: The ancient Romans would often make a vow -- "If you do this for me, then I will give you something (create an altar, hold ritual games, sacrifice livestock)." The idea with vows is that payment is only rendered (to the gods) after the deity does something that the person wants.