While Apple Music is a streaming music service, you can store music locally to listen to when you are offline. In the Music app on iOS, look for the cloud download button (looks like a cloud with a down arrow) when you are viewing a playlist or album. Tap that button to download and keep those songs for offline listening. The button will change to a iPhone/iPad icon with a checkmark inside it when the download is complete.
Mac Video Tutorials and Tips for Apple Users
