What key role those a cost-benefit analysis play? How is it used?

Computing, Analysing & Comparing : 'Benefit' of projects per unit 'Cost' incurred.

Explanation:

Cost Benefit Analysis is used to ascertain Benefit of a decision with regards to its cost. The decisions might be various : investing in a project, hiring a labour etc. The cost & benefits of the decision are measured in 'net present value', as costs / benefits (specially) might be scattered over a long period of time, & they need to be adjusted for price change then.

Benefit - Cost Ratio (as per Cost Benefit Analysis) : =

Total Benefit in Net present value

Total Cost in Net present value

If a project / decision has higher Benefit - Cost ratio, it provides more benefit per unit of cost & vice versa in case of low Benefit - Cost ratio. A project with high Benefit - Cost ratio would be preferred over the one having lower benefit - cost ratio.