There are several ways to share Kindle books:
1) You can always share books with someone on your amazon account. Most
books can be on 6 devices at the same time within 1 account. So, if you, spouse, kids all share an amazon account with kindles, tablets and so on then you can all read the same books. (More to come on blocking content on the kids' devices!)
2) Some books are lendable - one time only, for 2 weeks max.
This has been available for a few years. If it is available for a book (publisher's discretion) then the book page on amazon will say "Lending Enabled." See this old post for "how to" lend the book to someone.
3) Now, we also have Family library that allows you to link with a totally different account & share kindle books! You don't have to share all of your books though and you can restrict access to your entire library. This is great if your spouse has his/ her own account! Visit Help for more details!