A Local deck is a deck that is on your device (phone, tablet, or computer). When you make a new deck, or download a deck to your device, that deck is Local.
AnkiApp also stores your decks in the cloud, so they're always backed-up. When you log in from a new device, decks you have used before appear as "Cloud" decks.
If a friend shares a deck with you, that deck appears as a "Shared" deck.
All 3 kinds of your decks are found on your My Decks screen, shown below.
