The plot of Kafka on the Shore has two strands, and in that way the book is stylistically similar to the much earlier Hard Boiled Wonderland and the End of the World. In this book, though, both stories take place in the 'real world', though both at times dip into another dimension.
Trying to find the 'meaning' here is always going to be tricky, and is possibly not the point. This book is possibly Murakami's wackiest one yet. This wackiness puts a lot of people off. But the trick is to just go with the flow - the narrative thumps along at a cracking pace - and accept all the absurdities.
This 'other dimension' in the book is entered via the 'Entrance Stone'. To put it simply, characters in the story can enter this other dimension in order to freeze in time something they don't want to lose. One part of them lives on forever in this frozen moment while the other half continues in the real world, grows older, etc. This half, in the real world, seems somehow 'empty' (e.g. Saeki, Nakata). One odd consequence of characters leaving half of themselves behind is that their man/man, man/woman character besomes split, leaving only 'half a shadow'.
Saeki chooses to split in two, so that half of her can remain with her boyfriend, who is still alive and in love with her. Nakata does it too, but he doesn't seem to choose it, as Saeki does.
Kafka nearly does the same thing, but doesn't quite. He goes through the Entrance Stone in order to remain with an alive Saeki. But, crucially, she gives him the opportunity to learn by her mistakes, and helps him choose, by himself, not to remain there, leaving half of himself behind. Instead, he faces up to reality, and returns whole to the real world.
Basically, the book is about learning to accept the inevitable changes affected by time, and learning to let things go and not to hang on to them - a very Buddhist message.