The difference between carrying value and market value is that the carrying value of an asset is the original cost less the total accumulated depreciation associated with that asset, while the market value of an asset is based on supply and demand and perceived value of that asset. The carrying value and the market value of an asset can vary substantially.
The carrying value of an asset is recorded on a company's balance sheet. In each accounting period, the company records depreciation expenses related to an asset on its income statement. In the same period, a company's accumulated depreciation account on its balance sheet increases by the same amount. Accumulated depreciation is the sum of total depreciation expenses associated with an asset. Accumulated depreciation is also a contra asset account and has a credit balance rather than a debit balance. Since it is a contra asset account, adding it to a fixed asset account reduces the original cost of a fixed asset to its carrying value.
On the other hand, the market value of a fixed asset is not related to the values on a company's balance sheet or income statement, but it is the reasonable amount a company can expect to sell the fixed asset for on the open market.
For example, say a company buys a piece of equipment for $300,000. Each month, the company recognizes a $10,000 depreciation expense. After five months, the company decides to sell the piece of equipment, but it only receives offers of $200,000. The carrying value of the asset is $250,000, but since it can only reasonably sell the piece of equipment for $200,000, the market value of the asset is $200,000.