The days' sales in inventory tells you the average number of days that it took to sell the average inventory held during the specified one-year period. You can also think of it as the number of days of sales that was held in inventory during the specified year. The calculation of the days' sales in inventory is: the number of days in a year (365 or 360 days) divided by the inventory turnover ratio.
For example, if a company had an inventory turnover ratio of 9, the company's inventory turned over 9 times during the year. If we use 360 as the number of days in the year, the company had (on average) 40 days of inventory on hand during the year (360 days divided by the inventory turnover ratio of 9).
Since the inventory turnover ratio reflects the average amount of inventory during the year, and since sales usually fluctuate during the year, the days' sales in inventory is an approximation.