There're 2 things that you can share:
(1) Share what book you are reading: to do so, while you are reading a book, tap on the center of the device's display, you will then see the options pop up. Tap on "More" and then "Share".
(2) Share a quote or a sentence: to do so, while you are reaing a book, touch and hold to select a sentence, you wil then see the options pop up. Tap on "Share".