First of all it is important to make sense of what negative numbers mean. In some situations negative numbers don't make any sense. If you have £100 in your wallet and you keep removing money to pay for things, you will have less and less money, until eventually it is empty, (ie you will eventually have £0). You obviously cannot remove any more money once your wallet is empty and it makes no sense to say something like you have -£20 in your wallet! If however you spend all of the money in your bank account, you may still be able to take out more, in this case the bank lends extra money to you. A bank balance of -£20 does make sense, it means that you owe the bank £20!
Other examples of uses of negative numbers.