When you press the download button and is redirected to Dropbox then usually a window pops up on the screen asking you to sign up / login. Just tap outside the box in the dark area to skip this option. Then click the top-right corner on the download button to download the item.
iOS: http://www.wikihow.com/Download-Minecraft-Maps#Installing_Maps_on_iOS
iOS: http://www.wikihow.com/Download-Minecraft-Maps#Installing_Maps_on_iOS