What is the meaning of the phrase "slam home"?

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.

Slam is a verb denoting a quick forceful physical action that quickly achieves its goal, such as slamming the door shut. Whisk! Boom!

https://www.dictionary.com/browse/slam

Home in this case means "the intended destination" or "where it belongs".

Slam dunk is a similar expression in basketball, denoting a forceful dunk shot.

Slam denotes intensity, as you can see from the examples here:

https://www.lexico.com/en/definition/slam

It brings to mind the phrases related to 'grand slam' like these:

https://www.lexico.com/en/definition/grand_slam

And I haven't heard 'slam home' but I feel like it comes from baseball in which a grand slam results in all the batters reaching home plate.

Regarding your examples:

It slams home a sense of what the wars were like.

'Slams home' means that 'it' makes clear to an extent that nothing else had to that point, the subject of 'what wars were like' - achieving the goal of understanding. That goal achievement is like a home run.

To slam home the point, a guy from the State Department read our evening's agenda.

The guy from State Department did something unusual (read our evening's agenda) to achieve his goal (making the point) effectively, when nothing else would have that effect.