From Amazon’s press release:

Amazon today announced that Prime members in the U.S., U.K., Germany and Austria will now be able to download movies and TV episodes, including award-winning Amazon Original Series, to iPhones, iPads and Android phones and tablets for offline viewing, at no additional charge. Amazon Video is the only online subscription streaming video service that enables downloads of titles, meaning unlike other subscription streaming services such as Netflix, Prime members can enjoy movies and TV shows as part of their membership even when they don’t have an internet connection available.

Amazon Prime just keeps getting better. This will be perfect for traveling when internet connections could be unreliable.