In short
MRP is a planning method that calculates which materials are needed, when and in what quantity, based on demand, the bill of materials and inventory.
MRP combines the master production schedule, the bill of materials (BOM) and on-hand inventory to derive net requirements. The output is purchase suggestions and production work orders.
A well-run MRP reduces both excess stock and stoppages caused by material shortages. The prerequisite is an up-to-date BOM, accurate lead times and reliable inventory records.
Today MRP is usually part of a production management system, together with capacity planning, shop-floor tracking and costing.