Goodwill is technically the value of an entity over and above the value of its assets.
That is to say that if firm, according to its book assets, was valued at £4m but was bought for £5m then once the £1m difference would appear on the balance sheet as goodwill.
More practically speaking it reflects the value of intangible assets such as a great brandname, intellectual property rights or employee relations.
In the example above imagine the company makes tasty breakfast cereals at the moment. Once bought they could apply their name to other products such as cereal bars or fruit drinks which would command a price premium. It is this value that goodwill tries to capture on the balance sheet.