What's the owner of SqlServerAgent job for? What is the possible use of owner of an SQL Server Agent job, I wonder?  

Removed, and left it blank and the job still succeeds
The job owner determines the execution context of the job's steps.

For a T-SQL job step: If the job owner is a sysadmin then the step will execute as either the SQL Server Agent service account or a specified database user (set on the Advanced page of the Job Step Properties dialog). If the job owner is not a sysadmin then the step will execute as the job owner.

For other job steps: If the job owner is a sysadmin then the step will execute as either the SQL Server Agent service account or a specified Proxy. If the job owner is not a sysadmin then the step will execute as a specified Proxy (which requires the job owner to have permission to use the proxy). 

A SQL Agent Proxy is created based on a SQL Server Credential which stores the secret associated with some external security principal. For example, sysadmin Kim creates a Credential for ADVENTUREWORKS\Bob and then creates a Proxy based on that Credential. She makes the Proxy active for the CmdExec subsystem. She gives (nonsysadmin) Qin the rights to use that Proxy. Qin can now create a CmdExec job step that executes as ADVERNTUREWORKS\Bob. 

See Implement SQL Server Agent Security in Books Online.