Make sure you're connected to Wi-Fi
If you're trying to download an app using your cellular connection, that might be the problem.
By default, the iPhone won't attempt to download an app that's more than 200 MB in size so that it doesn't use too much data from your wireless plan. Cellular networks can also be generally unreliable for downloading large files.
To eliminate this potential problem, go somewhere with Wi-Fi, connect to the network, and try again. For instructions on connecting to Wi-Fi, see our article, "How to connect your iPhone to Wi-Fi in 2 different ways, to either a visible or hidden network."