The story revolves around a group of children of the gods who spend their summers at Camp Half-Blood, where they are protected and learn to harness their gifts and how to fight monsters. Camp Half-Blood has 12 cabins for each of the major gods who have a throne on Olympus. The gods maintain the laissez-faire attitude they've typically had towards their children, believing that maintaining a distance is better for them.
The books keep their Greek myths in place and respects the classic literature. It will take some liberty with things when it needs to to make things fit the book's premise. For example, monsters are never truly killed forever, they will eventually reappear. This is necessary so that the half-bloods get to encounter those famous Greek monsters despite the fact that other heroes in the past already killed them.
The books also take some liberty with the characterizations of the gods. Poseidon appears like a fisherman. Apollo appears as a late-teenager who drives around the sun chariot, which can transform between different vehicles. He prefers to drive some type of American muscle car. He's filled with bravado and has a tendency to spout out horrible haikus. Apollo is something of the hilarious edge case when it comes to godly representations. The others are not so extreme.
The books are writter for a young adult audience. So for those of you who are non-young adults, the writing may be somewhat juvenile. My biggest problem is that the foreshadowing was a little heavy handed. I never got one of those classic Harry Potter end-of-book reveals that ties everything. For example, one big question at the beginning of book one is "Who is Percy's father?" If you pay attention at all, you'll easily surmise who it is. This spoils the eventual reveal to an extent.
The books are quick reads. I read all five of them in the span of roughly ten days. If you like Greek mythology and are willing to take some small liberties with it and don't mind a writing style that isn't suited for your reading level, I think you'll enjoy these books.
There is a follow-up five book series called The Heroes of Olympus that is currently in progress. The reading level for these books is higher than the reading level for the original series. I've read both of them and they've been quite enjoyable so far. It will unfortunately be a long wait for the rest of that series to conclude. Furthermore, there is an Egyptian mythology themed trilogy called the Kane Chronicles that Riordan is also writing that I know very little about.