"Lower of cost or market" is a method of valuing inventory.
Generally, the value of inventory is based on the amount paid when it was purchased (cost).
Sometimes, the value of that inventory goes down due to becoming obsolete or showing signs of wear. When this happens, the business that owns the inventory has the option to take a deduction for the fact that the inventory can only be sold for less than it's original purchase price. When this happens and the business writes down the value of their inventory, this is considered the market price.
A business will usually elect to report their inventory at "lower of cost or market" to take advantage of writing down the loss in the value (to less than what they paid) of certain inventory items.
