Kohei Nozaki's blog 

Assume that there is a job execution which is STOPPED on the Job Executions table like following. let's see a drop-down list at right end of the row. you can take some actions for each job executions with this "Action" drop-down list.

This drop-down list contains some actions like following (for STOPPED one).

There are 3 actions available. "Restart" means restarting this execution as a new execution but inherit job instance from previous one. "Abandon" means abandoning this execution as won't be used again. after abandoning, restarting will be impossible. "Re-execute as new instance" means opening "Start Job" window with inheriting both of job name and job parameters of selected instance. also "Stop" is available for running executions.

After selection of Restart, pop-up window will be appeared like following.

This window looks similar to "Start Job" window, but Job Name editing is prohibited because this is about to restarting of previous execution. you can edit Job Parameters as well as regular job execution but initial value of them will be inherited if they exists in previous execution.