A cost object is a tangible input for a product manufactured/service provided, like labor or material. For example a cloth manufacturing firm requires some amount of predetermined labor and predetermined raw material for any amount of cloth being manufactured. The cost of employing labor can be directly fixed as "per man per hour" or "per man per day per hour per minute per annum", so the labor is a cost object as you can directly associate cost with it. Similarly the raw material like cotton or threads or fabric can be another cost object. Other examples may include services provided by another firm, for example a transportation company/ courier company can offer some service to all customers at a fixed rate. so the cost can be directly associated with it and the company/service can be then called as cost object.
Generally, cost object term is used for fixed Cost components of total cost otherwise any thing which is incurring some cost can be called as a cost object like an Advertisement.