Lincoln chooses his words carefully to evoke the maximum emotional response from his audience, here and in his other famous speeches.
His point is that we, as Americans, are not just a nation but a kind of meta-family, bound together not just historically but in some sense biologically. "We," the present population, are a kind of child, so a term that refers to biological reproduction, "conceived," is used. Those who founded the country were not merely the "founders," or the "forefathers," or even the Founding Fathers, as we normally say in our own time. They are "our fathers." The use of the word without elaboration or qualification conveys the actual idea of fatherhood beyond the mere metaphorical significance usually intended in such a context. And this, of course, fits with the literal idea of a conceiving or a conception, where the words suggest not only their literal biological meaning but also have religious overtones in the context of Christian belief. With these terms, Lincoln taps into the primal emotion at the source of human life—the eternal conception of man, woman, and child—and this forms the basis of his visceral appeal to the listener and the reader.
It has been pointed out that Lincoln's phraseology often derives from the King James Bible, though he was evidently a freethinker himself. To say "four score and seven years ago," rather than "eighty-seven years ago" or "in 1776" lends a gravity to the address in the very opening phrase which it would otherwise not have. It's also significant, as a corollary to the basic idea of "life" being "conceived," that he should say "brought forth on this continent." This evokes the mythological trope of creation as the result of a union between the "masculine" Sky (Ouranos in Greek) and the "feminine" Earth (Gae). Lincoln is therefore invoking both the concept of man-woman-child and the creation story of religion and myth in his appeal to the audience. He views the United States, and its survival, as holding an infinite, eternal value for not just Americans alone, but for the world.