Answer:
In accounting, agency costs are the costs of hiring an agent in order for him/her to act on behalf of a principal. In finance, agency costs are much broader since they imply costs that may appear due to conflicts of interests between the agent and the principal. E.g. a manager who seeks to accomplish short term goals in order to collect a bonus but hurts the long term objectives and goals of the stockholders.
Agency costs of financial distress refers to the costs associated with conflicts of interest that may result in a company being insolvent, specially in the long run. This type of costs are not necessarily related to operating costs, instead they result from management decisions and strategies, e.g. higher cost of capital or debt, or even excessive spending.
Agency benefits of leverage result from stockholders benefiting from the agent's decision to keep equity low, and if needed, obtain financing from debt sources.