I assume that the burden rate in inventory refers to a manufacturer's indirect manufacturing costs, which are also referred to as factory overhead, indirect production costs, and burden. In the U.S., a manufactured product's cost consists of direct materials, direct labor, and manufacturing overhead. Since manufacturing overhead is an indirect cost, it is usually assigned or allocated through an overhead rate or burden rate. Two examples of an overhead or burden rate are 1) a percentage of direct labor, and 2) an hourly cost rate assigned on the basis of machine hours.
A product's manufacturing cost, consisting of direct materials, direct labor and manufacturing overhead, is used to report the cost of goods sold and also the cost of units in inventory. Therefore, if you look at the detail of a product's inventory cost, you may see the manufacturing overhead being assigned or applied to the unit through a burden rate.