In management accounting relevant cost are those costs which are important or relevant for the future business plans. Relevant cost are often those cost which will be incurred if company decides to do something, in other words all historical cost are not relevant cost because they have been already incurred and therefore a company will look into future cost rather than historical cost to take any decision for future business projects.
So for example if a company is planning to increase the production of its products it would want to see only relevant cost associated with such decision. In this case if the company already has machinery needed to produce that good, it will not look into the cost associated with that of machinery. Company will rather look into the cost associated with raw material and labor needed to produce such goods and incremental benefits associated with such decision.
Relevant cost can be of significance importance when company has many alternative choices or projects and it is not sure which project is beneficial than a detailed analysis of relevant cost can help the company in choosing that project which will give maximum return to the company.