My own understanding on this:

Through the process of correctly learning Christian Science, the Christ becomes uplifted in our thought, which then draws our own thought up with it. Our ever-increasing understanding of Christian Science — and the confidence we have gained from applying and proving it — is what we will make use of to give treatments. Meanwhile, our spiritual sense becomes attuned to divine Mind, while simultaneously allowing us to be more discerning of the subtle ploys of animal magnetism which say that we and mankind are separate from God. This is how we begin to successfully “Stand porter at the door of thought.” (S&H, p. 392)

Then, as we look out to see the dangers which the Adam-dream seemingly presents to mankind (the watching), we then can apply the truth of Christian Science to nullify these supposed errors (the treatment). Mrs. Eddy has said, “The treatment is through God with us.” (Fragments, p. 163) As we are victorious in this, we will gain peace because we have in this moment proven our faithfulness to the one Mind, and the effectiveness of Christian Science (the demonstration).

However, as Christ Jesus taught us, not every heart is open to a Christian Science treatment at this time. He put some out of the room so he might heal others, and specifically taught us to never “cast ye your pearls before swine.” (Matthew 7:6) Because of this, the treatment must go forth from a thought filled with complete confidence that the Word of God will heal and bless and meet the need of those who are receptive. Just because a watch happened, and the entire world is not healed of all its ills, does not mean Christian Science does not work. Mrs. Eddy has said, “Either here or hereafter, suffering or Science must destroy all illusions regarding life and mind, and regenerate material sense and self.” (S&H, p. 296) Let us trust that the suffering has made some ready right now for the Science — just as it once made us ready — and know that the treatment will reach these people and it will “not return unto [God] void.” (Isaiah 55:11)