What's the owner of SqlServerAgent job for?

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.

(edit: Although this answer was accepted, and is valid, please ensure you read the other answer by @Greenstone-Walker since it has excellent information)

As Billinkc noted, a job can be edited only by its owner or members of the sysadmin role. And as Shawn Melton noted, removing the owner from the job simply ensures your login will become the owner. You can see this by looking at a system stored procedure in the msdb database: exec msdb.dbo.sp_help_job @job_name = 'somejob';

Books Online has an article about SQL Server Agent Job Security entitled "Give Others Ownership of a Job" which describes the process well.