As Donald Barthelme's short story "A City of Churches" focuses on the theme of absurdity, it is certainly a mystery as to what Cecelia means when she says towards the end, "I'll dream the Secret." But there are a couple of meanings we can deduce based on the surrounding text.
One thing Cecelia says just after speaking of dreaming "the Secret" is, "I'll dream the life you are most afraid of." One absurdity found in the short story concerns the fact Prester truly is a "city of churches"; it is a city made up of absolutely nothing but churches. Every shop, every dwelling place, every business is inside of a church. Since this is the case, it can be seen that the citizens of Prester do not separate any aspect of their daily lives from church, from their religion, and, more specifically, from the tenets of their religion. One might argue that, since the above is the case, the citizens are not free to live any life they choose. Hence, in saying that she'll "dream the life you are most afraid of," she is saying that she'll dream up a life that is completely free of religious constraint; one might even go so far as to say she'll dream of a life completely free of moral restrictions, possibly even a life of crime and murder. Hence, it is possible that when she says "the Secret" earlier, she is referring to her own secret understanding that life without religious constraints is possible, a belief that Mr. Phillips would reject.
It can also be noted that just before Cecelia speaks of "the Secret," Mr. Phillips declares that the townspeople are "discontented ... terribly, terribly discontented. Something is wrong." One can argue that their discontent stems from the fact that the townspeople do not connect religious values to choice--they are not religious because they choose to be; they are religious because they are apparently forced to be, which is the exact opposite of being religious. Religion stems from faith; faith can only be obtained through one's free will. Hence, one can conclude that Cecelia sees the absurdity of their enforced religious tenets, and in referring to "the Secret," she is referring to her own secret knowledge that contentment can only be achieved through pursuing one's own choices, not by being forced to conform to tenets, something Mr. Phillips would again object to.