The Gallery screen shows all your sketches you have stored on your iPhone / iPad. Tap and hold on a sketch for options to rename, duplicate, move to folder, or delete. Tap the "new sketch" button of course to start a new sketch. Tap and hold the "new sketch" button for the option to load your last auto-save if you accidentally discarded changes. For a demonstration of creating and using folders, check out this video on YouTube.
You can bulk select sketches and export them in different file formats. Use the .sketchClub format and AirDrop to easily move sketches between your devices. Check out Transferring Sketches.