Put simply, it's the scientific application of God's laws to the human need. The science itself has always existed, but it was discovered in 1866, when Mary Baker Eddy realized there were actually divine laws behind Christ Jesus' healing work, and that these laws can still be demonstrated today.
That's what everyone wants to know--it's a great question!
Generally speaking, we consider something scientific if it can be proven through experimentation, if the results can be repeated, and if those repeated proofs point to general laws operating all around us.
There are laws of God that govern the universe. We find them in the Bible, especially in the teachings and healings of Christ Jesus, his disciples and apostles, and the prophets. And we can prove them in our lives to the extent that we understand them and know how to apply them. Just like we can with the principles of math or music.
You can visit ChristianScience.com for more details...
...or you can go straight to the source: the textbook on Christian Science, Science and Health with Key to the Scriptures by Mary Baker Eddy.
Here are some ways to do that:
You can find and visit your local Christian Science Reading Room using the directory located here. They have copies you can read while you're there, as well as ones to borrow or purchase.
"The time for thinkers has come" (p. vii).
"God is not influenced by man. The 'divine ear' is not an auditory nerve. It is the all-hearing and all-knowing Mind, to whom each need of man is known and by whom it will be supplied" (p. 7).
"Atonement is the exemplification of man's unity with God" (p. 18).
"Love enriches the nature, enlarging, purifying, and elevating it" (p. 57).
"God, good, being ever present, it follows in divine logic that evil, the suppositional opposite of good, is never present" (p. 72).
"There is but one real attraction, that of Spirit" (p. 102).
"The vital part, the heart and soul of Christian Science, is Love" (p. 113).
"Spiritual causation is the one question to be considered, for more than all others spiritual causation relates to human progress" (p. 170).
"The best sermon ever preached is Truth practiced and demonstrated by the destruction of sin, sickness, and death" (p. 201).
"Love, the divine Principle, is the Father and Mother of the universe, including man" (p. 256).
10. Science of Being
"Man's genuine selfhood is recognizable only in what is good and true" (p. 294).
"Does divine Love commit a fraud on humanity by making man inclined to sin, and then punishing him for it?" (p. 356).
"Stand porter at the door of thought. Admitting only such conclusions as you wish realized in bodily results, you will control yourself harmoniously" (p. 392).
"Love for God and man is the true incentive in both healing and teaching" (p. 454).
14. Recapitulation [Q&A chapter]
"Man is idea, the image, of Love; he is not physique" (p. 475).
"Spiritually followed, the book of Genesis is the history of the untrue image of God, named a sinful mortal" (p. 502).
16. The Apocalypse [i.e., the book of Revelation]
"At all times and under all circumstances, overcome evil with good" (p. 571).
"ANGELS. God's thoughts passing to man; spiritual intuitions, pure and perfect; the inspiration of goodness, purity, and immortality, counteracting all evil, sensuality, and mortality" (p. 581).
"ASTIGMATISM AND HERNIA HEALED - It is nearly five years since I bought my first copy of Science and Health, the reading of which cured me of chronic constipation, nervous headache, astigmatism, and hernia, in less than four months" (p. 601).
If you'd like to dive right in, here's a chapter guide to Science and Health,
complete with links to the chapters and a quotation from each.