A Job under Process Explorer refers to Win32 Jobs. More information about this feature can be found here.
So,
1. What is a Job?
As above.
2. What should I know about these things?
If a job fails or becomes unstable, all processes it manages will become unstable or crash immediately.
3. Why would (you|one) use them?
They are interesting tools if my application/system fires up several processes. I can centralize certain tasks in one job and attach all processes to it. Like gracefully terminate all processes, manage their working sets, etc.
4. What scenarios should they be used?
Never did anything worthed using them. But as above. In applications or complex systems that fire up several processes. Under Chrome, for instance (since this is where you are seeing a job), it is quite possible the job is managing each process that is fired when you open a new tab.
5. What APIs are used?
The Win32 API