First method does not store the number itself anywhere. Let's assume that you store apples. I come and ask you "How many apples do you have?". To answer, you go and count every single apple one by one and return me the number. It's very easy if you have a small number of apples, but if you have, let's say, 5000 apples - you can see how long it may take.

Second option is you keeping a track of how many apples you have in stock by having it written down somewhere. If I ask you "How many apples do you have?" you just pull out your notepad and tell me the number. If you give me an apple, you just adjust the number you have written down already.