How does resource leveling keep a project on schedule?

Resource levelling (predetermined resource levels are never exceeded) is only a Project Management technique to make efficient utilisation of resources. The key to keeping a project on schedule/under control is to utilise resource levelling in the context of planning ahead in terms of the people, skills and equipment you need at the appropriate times (thus keeping the resource managers happy), utilising any available float, understanding your project priority in the wider company scheme (with respect to other projects should you need to make a call on additional resources) and having the flexibility to vary project milestones and (if required) end-dates if you don't get allocated the necessary resources.