An Essay in Aid of a Grammar of Assent (commonly abbreviated to the last three words) is John Henry Newman's seminal book on the philosophy of faith.
Newman's aim was to show that the scientific standards for evidence and assent are too narrow and inapplicable in concrete life.
He wrote this book against the background of British Empiricism which restricted the strength and legitimacy of assent to the evidence presented for it.
So while the regular unlearned Christian, or anyone for that matter, may not be able to conceive that God is one and three, the words of the propositions that define the doctrine are clear and intellectually accessible and assent may legitimately follow.
This is an inferential statement as opposed to "The car in front of the house is red," which is an assertion that can be assented to because it can stand on its own.
Natural inference is when the individual, in a simple and whole process, grasps the antecedent conditions and conclusions instantaneously.
It is the faculty of the human mind that closes the logic-gap in concrete situations and thus allowing for assent.
Thus, to close that gap between converging probabilities and full assent, one needs the aid of the Illative Sense to attain certitude in specific situations.