How do I sync my iBook app across my devices?

It would have been very helpful if you told us your exact symptoms.

Without knowing that, a few thoughts come to mind:

• Make sure your iPad and Mac use the same Apple ID.
• Make sure your Mac's iBooks app is signed in to that Apple ID (Store > View My Apple ID from iBooks' menu).
• Try Store > Check for Available Downloads from iBooks' menu.

Presumably you are talking about books purchased from the iBooks Store.

Oh, since you posted in the MacBook Air forum, I never would have guessed you are talking about sharing documents between an iPad and an iPhone.

Also your comment "I download a PDF into iBook app from the iPad" makes it sound as if you did not purchase this item from the iBooks Store.

Therefore, the only hope is that you would sync the iPad to your Mac using iTunes, then sync the iPhone to your Mac using iTunes. After syncing your iPad, see if the PDF is in fact in iBooks on the Mac.

One other thought -- since you have an iPad Air and an iPhone 5S, you could use iOS AirDrop to share the document.

See: http://support.apple.com/kb/HT5887