As Andy Bonner points out in a comment beneath the posted question, "slam home" is a variant of the more common idiomatic phrase "drive home." Here is the entry for that phrase in Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013):
drive home Make clearly understood, make a point, as in The network news programs drive home the fact that violence is a part of urban life. This expression uses the verb drive in the sense of "force by a blow or thrust" (as in driving a nail). Samuel Hieron used it in Works (1607): "That I may ... drive home the nail of this exhortation even to the head."
So it appears that the drive-a-nail sense of "drive home" may have been the original metaphor behind this idiom. The "head" in Hieron's quotation is not the reader's or listener's head, by the way, but the nail's.
To similar effect, John Ayto, Oxford Dictionary of English Idioms, third edition (2009) has this entry:
drive something home make something clearly and fully understood by the use of repeated or forcefully direct arguments. | The verbs hammer, press, and ram are also used in pace of drive.
Ayto's discussion suggests that slam is a less common alternative to drive in variant forms of the expression than several other verbs, at least in the UK. I have heard "slam home" used in the context of hockey, soccer, and basketball games, where a player strikes the puck or ball into the goal or net—usually from close range. But whether the image that the author had in mind was of a carpenter driving a nail or a basketball player dunking the ball for two points, the figurative sense of "slam home" as making something clear beyond any mistake remains essentially the same.