Good clean fun for kids...and for adults, too.
Other folks have already noded up decent introductions to the stories overall, so I won't waste time on that. What I would like to note is how tightly-plotted and well-written these books are. Without giving too much away, a name is mentioned offhand in the first or second chapter of the first book--and then never mentioned again in either the first or second book. And yet, the character of that name comes to major prominence in the third book--but only when you go back to that first one do you quite realize it.
The books are full of things like that--foreshadowing, sometimes very specific foreshadowing, abounds. Tantalizing hints and clues are given about things to expect in future books. References are made to events in prior books, casting things that seemed unimportant at the time in a whole new light. Characters turn out to be not what they first seemed, sometimes in astonishing ways.
And let's not forget that they grow in size and complexity as they progress in the series--to the point where Goblet of Fire is 734 pages long, and over two inches thick...a rather intimidating volume--but by the time they get there, kids want to read it.
As for the Fundamentalists who claim that Harry Potter is satanic--well, these are often people who will claim that any fantasy is satanic--even The Lord of the Rings and The Chronicles of Narnia, which were written by two of the most renowned Christian writers of our time. Apparently, to these people, the road to Hell is paved with using one's imagination.