The Review period gives Amazon the ability to ensure your book is formatted correctly and complies with their guidelines before becoming available to readers.
Typically, the review takes three days, though in some cases, it could take as long as a week. There are also times your book can go live much quicker.
The usual delay in getting through the review process is that the book or its cover is not formatted correctly. Another bump in the road is if there is content in the book that violates the KDP policies. In case there are errors or points to address, Amazon will notify you via email so you can make the adjustments needed, which, when done, you will need to resubmit your book to be reviewed again until it goes live.