I'm getting to this one quite late, though I know it's had a fair amount of good things said about it.
To be tautological for a moment, Goblin Slayer slays goblins. He's slayed goblins for a very long time, in vengeance for them slaughtering his entire family when he was a child. He could only hide as they murdered his parents and sister, leaving nothing but his one friend and the burning fires of hatred for the goblin race.
He's basically the Batman of this fantasy world. Both in his tactics and his personality. He believes in a scorched earth policy, and will only be happy when every goblin is dead. This tends to set the initial tone of the series, being a grimdark version of the usual fantasy anime, in which people don't have the easiest time, and the "hero" is probably some sort of sociopath.
So we've got a slayer who is prepared to fight dirty, and that means he's an excellent person to send against the goblins. They are supposedly simple, weak creatures, but they have "a certain low cunning" which makes them able to set traps and engage in simple strategies. This can be remarkably effective against novice adventures, and is reminiscent of Tucker's Kobolds.
This means that the fights in this have actually quite a pleasing amount of pragmatic strategy. He's happy to set fire to corpses and smoke goblins out of their holes. He'll stop the problem at the root (which here means killing goblin babies). And he'll set up traps of his own, with the assistance of Priestess, who he rescued from a particularly horrible fate in the first episode.
That first episode is unexpectedly graphic. The show comes with a content warning, but that doesn't really prepare you for goblins capturing women for breeding stock and forcing themselves on them in the middle of a battle. Bit too much for some people, I might think, and does feel a bit unnecessary.
The main problem is that the series doesn't quite know what mood it's trying to set.
The first episode sets the standard for a properly gritty story, with vicious fights, the feralistic nature of the goblins and the fact that the heroes are not playing nice. But at the same time, they stop to have a pleasant chat around the campfire, or get hit on by the head of the adventurer's guild. It's possible to use moments of lightness to contrast with the overall bleakness, but that isn't what this does. Instead, it seems to have started with the idea of being horrible, but doesn't have the stomach to stick with it.
As the series runs on, it gets more and more light hearted. The ensemble that build themselves around Goblin Slayer all have silly behaviours (there's even an "aren't elves flat" joke, at the lowest point), and their mood sets Slayer up for a collection of deadpan punchlines throughout. It's trying really hard, and it nearly succeeds, but the tension never quite gets there. That is partly due to the main characters never feeling threatened, after that first encounter of Priestess in the goblin cave.
And there's still food porn.
I like what it tried to do. We've not had something actually grim in a while, and this is close. It runs a bit too heavy on the fan service, especially for a series which looks at the dark side of morality. And the animation is underwhelming at points, such as the out of place CGI on Slayer, and the repetitiveness of the goblins. But it builds a complex story, and has a lot going on in the world suggesting a decent depth. If you can get past the first episode, and enjoy the thought put into the combat, you'll likely enjoy the rest of it. Just try not to get too bogged down in the love triangle and the date where they eat ice cream.