When you divide, a number does not always divide perfectly. For example, 9 divided by 3 is 3. 3 goes into 9 exactly 3 times. But if you have 10 divided by 3, 3 goes into 10 three times (3x3=9). Because 3x3=9 and you still have to add 1 to get to 10, the remainder is 1. The same goes for other problems.
Because all numbers don't perfectly go into other numbers.
Say, for example, that you want to buy a skateboard that costs $50. You only have 3 20 dollar bills in your wallet, so you give the cashier $60 and he gives you $10 in change, because its IMPOSSIBLE to pay $50 exactly if you only have 20 dollar bills.
