An asset is anything that you own and has value. On the accountant's balance sheet, the assets you own are listed in the left column, and any liabilities and equity built is listed in the right column.
Robert Kiyosaki challenged this definition in his book Rich Dad Poor Dad. He claims in his book that an asset should put more money into your pocket, either by producing a positive cash flow, or through appreciation in value. Furthermore, he claims that a person's house is not an asset because the bank who holds the mortgage is earning the cashflow coming from the mortgage payments (which is shown as a liability on the owner's balance sheet). In addition to the house payment, the owner must also pay the property taxes to the government, and also pay the upkeep to maintain the house's value on the market. In short, the only houses that Kiyosaki counts as assets are those that appreciate in value (investment properties) or rental properties producing enough cashflow to pay the mortgage, taxes, and upkeep.