On mobile, Stardew Valley's save method is based upon the system used for PC, but with some additions to make it more suited to mobile devices.
The game creates a folder on the device for each save game. You can see this folder by connecting your iOS device to a Mac or PC running iTunes, as [[Saves#iOS_to_PCMobile (iOS)|outlined here]].
In that folder, there are three different kinds of save files which can appear - Standard Saves, Emergency Saves and Backup saves.