This extra ending is called the "accusative case". We will use this for specific direct objects.
If we were reading a specific book (THE book, MY book, THIS book, etc.) we would use accusative ("kitabı"). However, in this sentence, we are reading an unspecific book (A book), so the word stays in nominative case: kitap.
Also keep in mind that this is only for direct objects... so if the book is the subject of the sentence, we don't need accusative, even if it is specific. Ex. Kitap mavi. = The book is blue.
I highly recommend ignoring the app and only using the website, https://www.duolingo.com/ .
That will get you access to the tips and notes for the lessons and also access to the discussion forums https://forum.duolingo.com/topic/912 .
There's a very useful post pinned there which links to various other posts on various points of grammar: https://forum.duolingo.com/comment/7738932 "Turkish Grammar Portal [Under Construction]".
One of the posts it links to is https://forum.duolingo.com/comment/7738396 "[Grammar] Accusative Case".
Toss the mobile app. Embrace the website.