It's ostensibly an anti-war book. Vonnegut's talent lies in recasting the familiar in unfamiliar terms to highlight its absurdity. For example, this passage:

American planes, full of holes and wounded men and corpses took off backwards from an airfield in England. Over France, a few German fighter planes flew at them backwards, sucked bullets and shell fragments from some of the planes and crewmen. They did the same for wrecked American bombers on the ground, and those planes flew up backwards to join the formation.

The formation flew backwards over a German city that was in flames. The bombers opened their bomb bay doors, exerted a miraculous magnetism which shrunk the fires, gathered them into cylindrical steel containers, and lifted the containers into the bellies of the planes. The containers were stored neatly in racks. The Germans below had miraculous devices of their own, which were long steel tubes. They used them to suck more fragments from the crewmen and planes. But there were still a few wounded Americans, though, and some of the bombers were in bad repair. Over France, though, German fighters came up again, made everything and everybody as good as new.

When the bombers got back to their base, the steel cylinders were taken from the racks and shipped back to the United States of America, where factories were operating night and day, dismantling the cylinders, separating the dangerous contents into minerals. Touchingly, it was mainly women who did this work. The minerals were then shipped to specialists in remote areas. It was their business to put them into the ground, to hide them cleverly, so they would never hurt anybody ever again.

The above is from when the main character - unstuck in time - watches a war movie and then watches it again backwards. This backwards version is beautiful. Here's another excerpt, describing the plot of a fictitious book by a character, Kilgore Trout, who writes pulp science fiction novels:

It was about a robot who had bad breath, who became popular after his halitosis was cured. But what made the story remarkable, since it was written in 1932, was that it predicted the widespread use of burning jellied gasoline on human beings.

It was dropped on them from airplanes. Robots did the dropping. They had no conscience, and no circuits which would allow them to imagine what was happening to the people on the ground.

Trout's leading robot looked like a human being, and could talk and dance and so on, and go out with girls. And nobody held it against him that he dropped jellied gasoline on people. But they found his halitosis unforgivable. But then he cleared that up, and he was welcomed to the human race.

A rather blunt but effective metaphor for what humans can be brought to do in war and how people back home react to atrocities done for the sake of war.

Obedience,
Bane of all genius, virtue, freedom, truth,
Makes slaves of men, and of the human frame,
A mechanized automoton.
--Percy Bysshe Shelley

But on top of being an anti-war book, Slaughterhouse-Five also presents a broader philosophical outlook that is worth a ponder. As mentioned, the main character is unstuck in time - he finds himself sort of stepping outside the timeline and seeing his whole life as one completed, unbroken whole. Rather than a one-way trip through past, present and future, it is just a collection of moments, and in each one (i.e. the whole thing) we are aware and alive. Vonnegut explains it from another angle: it's as if humans aren't two-legged creatures but "great millipedes with babies' legs at one end and old peoples' legs at the other."

I recall when I was much younger and first heard the term hyperspace (space with more than four dimensions). I wondered what a four dimensional house might look like, and I thought it might look like a movie of a house over time. Each frame is a moment, and each frame captures the house at that moment - every board and beam, every molecule. In other frames, further down the movie reel, there are some different boards and beams, new molecules make up the whole. We still call it the same house, if it's similar enough to the old one, and say its identity persists over time. But then we could look at the whole movie reel and say that instead of having a house persisting through time, the reel itself is one object (a hyper-object) which has no time. It is frozen; it just is. And at different parts of the object, it looks different; i.e. a slice at one point or another will show a different looking house in the familiar three dimensions.

That's the fourth dimension: it's the familiar time dimension, but recast as a fourth spatial dimension. It doesn't necessarily change how things go down; it's just an alternate view, a new angle from which to inspect our existence. And Vonnegut explores it with his unique character (who has the added bonus of partially knowing everything in his 4D life-object no matter which point he is currently experiencing), which gives him the opportunity to expound on more general themes of life and death.

Which reminds me of one of my favorite Nietzsche quotes:

What if a demon were to creep after you one night, in your loneliest loneliness, and say, 'This life which you live must be lived by you once again and innumerable times more; and every pain and joy and thought and sigh must come again to you, all in the same sequence. The eternal hourglass will again and again be turned and you with it, dust of the dust!' Would you throw yourself down and gnash your teeth and curse that demon? Or would you answer, 'Never have I heard anything more divine'? -Friedrich Nietzsche

Indeed, as you watch Vonnegut's character go back to different moments of his life - some great, some not so great - and expound on the value of those great ones as places to revisit or stay, you begin to look at your own 4D life-object and think about how much of it is made up of truly flourishing moments.

But then, could humans ever truly be happy revisiting the same happy moments of their lives over and over, no matter how good? If Sisyphus' curse had been to live out eternity making love to the same beautiful woman over and over again, would it seem less abhorrent than his punishment of pushing a boulder up a hill over and over only to have it roll back down again and again for eternity? Maybe it does sound better, but I think there's still the issue that we humans constantly need new experiences, even if they're sometimes bad. We need the striving - we can't ever seem to reach a final goal and be happy and content with exactly how things are. We get bored. Humans were not meant for Heaven.

Thankfully that is only an issue for Vonnegut's character, whose experiences all happen in some sense partly outside his 4D life object - insofar as he is knowledgeable of other, "future" times even early in his life. If, rather, like Nietzsche frames it, we simply relive each moment over and over, but with the same ignorance every time, we couldn't ever get bored. It would always be just as new. In which case, is there any distinction at all between experiencing that moment once and experiencing it a million times, or an infinite number of times?

I don't know; the more I think about it, the more I suspect there is no difference at all. In which case, it doesn't matter whether Nietzsche's prophecy is right. We should live for the best moments there in those moments just for their own sake, for the sake of having a good experience right then. The 4D life-object is better that way, regardless of whether you want to consider something timeless like that to be a life relived over and over or a life-object lived once and all-at-once.