Array: A contiguous block of memory. When you know the position of the nth element of an array, you know that the elements at n+1 and n-1 are very nearby in memory.
Stack: A first-in-last-out data structure. A stack can be backed by most generic data structures (even arrays), but the linked-list type seems to be most common. You can think of a stack like a stack of playing cards. You can put a bunch of cards facedown on a table, and when you draw from the stack, you can only take the topmost card. The "first-in-last-out" means that the card that you put down first can't be removed until you remove all cards on top of it.
Queue: A first-in-first-out data structure. Very similar to a stack in regards to data storage. Think of this one like a line of people. The first person in the line is the first one to get out of it, and everyone behind them has to wait their turn.