Direct costs are those costs that cann be directly attributed to a product or product line, or to one source of sales revenue, or one business unit or operation of the business. An example of a direct cost would be the cost of tires on a new automobile.
Indirect costs are very different and can't be attached to any specific product, unit or activity. The cost of labor or benefits for an auto manufacturer is certainly a cost, but it can't be attached to any one vehicle. Each business has to devise a method of allocating indirect costs to different products, sources of sales revenue, business units, etc. Most allocation methods are less than perfect, and generally end up being arbitrary to one degree or another. Business managers and accounts should always keep an eye on the allocation methods used for indirect costs and take the cost figures produced by these methods with a grain of salt.
Fixed costs are those costs that stay the same over a relatively broad range of sales volume or production output. They're like an albatross around the neck of business and a company must sell its product at a high enough profit to at least break even.
Variable costs can increase and decrease in proportion to changes in sales or production level. Variable costs vary proportionately with changes in production/
Relevant costs are essentially future costs that could be incurred, depending on what strategic course a business takes. If an auto manufacturer decides to increase production, but the cost of tires goes up, than that cost needs to be taken into consideration.
Irrelevant costs are those that should be disregarded when deciding on a future course of action. They're costs that could cause you to make a wrong decision. Whereas relevant costs are future costs, irrelevant costs are those costs that were incurred in the past. The money's gone.