iReal Pro keeps playing in the background, so you can switch to another app (a PDF of the melody, a page of lyrics, or other practice material) without losing the backing track. This works on iPhone, iPad, Android and Mac.
Playback stops if you go looking for a song on YouTube, or in your own music, through Share > Search for on iPhone and iPad or Share > Find on Android, since that wants the audio for itself.
For more, see Play a song on the iReal Pro website.