The saves are stored as XML files on your computer or mobile device. They're stored separately from your game, so you can safely reinstall or update the game without losing them. On PC, they're shared between different copies of the game (e.g. if you buy it from both GOG and Steam).
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Each save has a folder like <tt>JonSnow_123456789</tt>, with two main files inside it: <tt>JonSnow_123456789</tt> and <tt>SaveGameInfo</tt>. Both files are needed to load the save.