IIRC, goodwill balance would only arise if there is an acquisition. The goodwill figure would be the difference between the acquisition price and the target company's net assets.

Fair value, on the other hand, could be more complicated and controversial. Fair value generally refer to the value given to an asset or liability. This is easy if all assets are buildings and cars and all liabilities are creditors. The question is, how do you value an asset that is hard to value or an asset that has no open market for it.

Is that rhetorical? Anyway, my attempt to answer it.

Goodwill is a kind of asset. It is intangible hence there is no physical form. Examples are like brand name and customer loyalty. Goodwill usually arises in the balance sheet when there is an acquisition of a company. For example A takes over B. A paid 10million. B's fair value is valued at 8million. The take over premium shall be treated as a goodwill and it would be entered in to the asset part of the balance sheet. I think both the IFRS and GAAP not does not allow amortisation. Not too sure about that. A quick google search would give you the answer.