There are a few different physical zones in the playing space. The battlefield(play area), the library(deck), the graveyard(discard pile), exile, and the Stack. The battlefield is just the space in front of you where you can lay out your permanents1 in whatever configuration you want. The graveyard is where all cards go when they have either been destroyed, used, discarded, ect. There are certain cards that can interact with other cards in the graveyard but that's something more complicated. The library is what's left of your deck after you draw your hand. Cards will refer to the deck as your library, just know that they mean your deck. Whenever you draw a card whether that being at the beginning of your turn or when a card says so you will draw from your library. Exile, which is not on the picture down below, can be anywhere as long as you and you opponent can distinguish it from the other zones. Exile is like the graveyard except it's more permanent and only very few cards interact with the cards in exile. Older cards also might say remove from the game but that is the same as exile.
1 Permanents are all cards that you play that stay in the battlefield. Creatures, Lands, Enchantments, Artifacts, and Planeswalkers are all permanents.