The first time you open the app, it will automatically pre-download all the audio files for your default language (probably English). Files that aren't downloaded will be streamed (downloaded temporarily on the spot) when you press play, so pre-downloading (best on a wifi network) keeps you from having to use your phone's data network while listening. You can change which languages are downloaded on the "Downloads" tab.
Version 1.4 of the LDS Music app, which will be released really soon (in the next few weeks), has a lot of new stuff, including both vocal and instrumental audio. You can join the "LDS Music for iOS" project here at Tech.LDS.org to contribute or listen in on the conversation.
Samuel Bradshaw • If you desire to serve God, you are called to the work.