A risk-benefit analysis is a process where you consciously evaluate the various risks and benefits of a decision in order to make the best possible choice.
There are several important concepts in that definition. First, you are expected to “consciously” evaluate the risks and benefits. This means that you go beyond your gut instinct, your initial impression, and seek out additional information that might affect the decision. This additional information might be factual (“There is a one in one thousand risk of a stroke without this surgery”), but it also might be emotional (“I’m more scared of heart surgery than we am of a stroke”).
The next concept involves the “various risks and benefits.” These should be as broadly defined as you need. Any risk or any benefit that affects your personal decision is a valid one. For example, if you are buying a new car, you might feel that the risk of global warming is important enough to include in your risk-benefit analysis.
Finally, the goal is the “best” possible choice. “Best” is defined by you and doesn’t have to be entirely rational. If you are particularly scared of planes, you might choose to drive across the country instead of flying, even though your risk of an accident is lower while flying.