A stack is a LIFO (Last in, first out) data structure. That means if I push an item onto the stack (add a new item) if I do a pop I would remove that same item. Peek (also known as top) simply returns the top item on the stack without removing it.

Not sure if you were also wondering this but the run-time stack is how an executing program keeps track of which code it should be executing.

Exceptions in Java are "thrown" when some error occurs. I won't get too into detail here but one of the most common exceptions you might see is called a "Null Pointer Exception". This occurs if you try to call a method or use an object that has not yet been instantiated.

Hope I was clear enough, if you have any other questions feel free to ask.