I Have the same issue on both iPad and iPhone but for 3 days now. It's annoying because downloading new apps does not work either. Had the same issue about a month ago and blamed it on having iOS 9 beta. Someone in a forum suggested logging out of my AppStore iTunes account, reset the iPad by rebooting and logging back into my account. That seemed to have resolved the issue.
This time it doesn't work though. iPhone even refused to let me log in telling me iTunes Store was having issues, iPad did log me in but did not resolve the download issue.
Safari also has issues logging me into the community here so I had to switch to Chrome which is a drag because it will not type properly in this window. I apologize beforehand for annoying typos. I hope they fixed it soon, whatever it is, 3 days is a long time.