Saving a job from the jobs manager is practically the same as saving the results of a search from elsewhere in Splunk. Splunk searches cause jobs to be executed, and the results of these jobs are saved by default for 10 minutes. When you save a job, it is kept longer - defaulting to a week. Saved jobs allow you to share search results with colleagues, or refer back to them as needed later on.
There is good information on the job lifecycle in the Knowlege Manager documentation, and TTL settings for jobs are configured in limits.conf.
