An employer is the person or organization that you work for. Can't find a job? Look at the bright side: you don't have to cater to the whims of any employer!
The verb employ means "to make use of." An employer hires an employee, or worker, in order to employ him at various tasks. A factory owner is an employer who might hire people to work on an assembly line. If you're a teacher, then your school is your employer. If you’re lucky enough to have a generous employer, then you’ll probably want to stay at your job for a while!