What is the "science" in Christian Science?

I'm not trying to debate the value of the religion or its practices, I am just curious how and why the term "science" became associated with this religion.

The word "science" is derived from the Latin word scire, to know. In that respect, Christian Science makes a neat parallel with the ancient Gnostic heresies (Greek gnosis, knowledge) that it resembles in certain basics.

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John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams

George Carlin would say that the expression is meaningless. As in "military intelligence"
...the words are mutually exclusive.

From the book "Science and Health with Key to the Scriptures" (1910 edition, re-published 1986), written by Mary Baker Eddy (founder of the"Christian Science Church"):Many imagine that the phenomena of physical healing in Christian Science present only a phase of the action of the human mind, which action in some unexplained way results in the cure of disease. On the contrary, Christian Science rationally explains that all other pathological methods are the fruits of human faith in matter, -faith in the workings, not of Spirit, but of the fleshly mind which must yield to Science.It is my guess that Mrs. Eddy was using the word "science" as just a synonym of "knowledge", trying to convey the idea of a specific healing knowledge revealed to her by God (she was a "spiritual healer"), and being herself a christian, her techniques became "Christian Science".
But I could always be wrong.

Yes, well, CS isn't particularly "Christian", either. There is, despite urban legend, a large common ground of Christian doctrine, shared alike by Eastern Orthodox, Roman Catholic, Anglican, Lutheran, Presbyterian, Methodist, Baptist, and many other sorts of Christians. Christian Science is incompatible with that common ground. In particular, the CS view of Matter is utterly at odds with the fundamental doctrine of the Incarnation.

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John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams

Along these same lines, why do most computer courses call themselves "Computer Science." Anyone who's ever watched a programmer or administrator at work knows that computer operation isn't a science. It's magic.

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"I had a feeling that in Hell there would be mushrooms." -The Secret of Monkey Island

Yes and no. There are many parts of Computer Science that are well understood by now -- sorting algorithms, secure key-exchange protocols, the parts of compiler design that can be handled by programs like LEXX and YACC, bulletproof two-stage transaction commit.... Only a fool ignores the work of real Computer Scientists when programming this sort of thing.

But, just as there are things that an engineer can do that a physicist can only wonder at, there are things that a programmer can do that are beyond today's Computer Scientist.

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John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams