An intangible asset is, to put it simple, an asset without physical substance. You cannot touch it. An intangible asset is something you only recognize within your accounts if your company can control the asset and you can determine the cost reliably. 

Examples of intangible assets are most often just computer software you acquired separately from the hardware and it’s in no way tied to a specific hardware, computer. Other examples of intangibles kept by companies are trademarks, certain rights etc. The way you’d treat an intangible on your balance sheet and income statement is the same as you’d use for tangible assets, property, plant and equipment with the only difference being the physical substance really. As with tangibles, if you determine that you can use an asset seemingly forever, it’s not amortized into expenses. Unless your local accounting framework says that you should not have intangible assets with indefinite useful lives, so please do consult with your local framework as there are some which clearly set restrictions for useful lives on intangibles.

As with tangible assets, consider acquisitions and whether you’ve actually obtained an intangible asset for your company.