Contribution margin answers a narrower question than profit margin: not "is this unit profitable after everything?" but "how much does each unit sold help pay down the bills that don't change with volume?" It's calculated per unit (or as a ratio, contribution margin ÷ price) and deliberately excludes fixed costs like rent or salaries.
This makes it the key input to break-even analysis — fixed costs divided by contribution margin tells you exactly how many units you need to sell before fixed costs are covered and every further sale is pure profit. A healthy contribution margin ratio also tells you how much cushion you have to absorb a price cut or a cost increase without losing money on each sale.