An asset represents a valued economic resource belonging to an economic agent - in either tangible or intangible form - that adds to the wealth of an individual.
Most commonly assets are a term commonly used when referring to financial institutions, as it appears on the balance sheets of these institutions.
For instance, the claims that banks have against economic agents represents what the bank owns on its balance sheet and therefore are marked down as part of their assets. For example a loan (advance) is an example of an asset that would appear on a bank's balance sheet as it is money that they have lent out to other parties but are expecting back into the bank in the future.