Intangible Assets are non-physical assets on a company's balance sheet
Intangible assets are assets that cannot be physically seen or touched. In general this includes things like intellectual property (such as patents and trademarks), brand recognition, and trade secrets. On the balance sheet, intangible assets add to the total asset value and, as such, are a component of the total book value.
While the value of intangible assets is harder to calculate than physical assets such as equipment or factories, intangibles have no less real value than their physical counterparts. There are several methods used in calculating the value of intangible assets, all of which rely on an accountant or accountants' estimates of worth.
In most cases, GAAP does not allow internally generated intangibles to show up on the balance sheet. For example: Coco-Cola corporation would not list the value of its brand on its balance sheet. On the other hand, if a company pays more than the fair value to acquire another company, the difference is shown as goodwill in the acquirer's balance sheet. Also, research-based companies, such as drug-manufacturers, are allowed to capitalize their research and development expenses -- since, in theory, research provides value long after it has been completed.
Some intangibles are amortized, i.e. written off, as expense over time. Under the U.S. GAAP goodwill cannot be written off as expense unless the company has a reason to believe that it has reduced in value. Amortization of intangibles decrease income of the company and hence offer tax benefits.
It should be noted that goodwill, while technically itself an intangible asset, can be listed separately on the balance sheet. In other words, a balance sheet may list intangible assets and goodwill separately or together.