You need to write that you left because you no longer wanted to work for the company. As long as there are a mutual agreement, there is no reason to explain more about it.
You should answer the question honestly and briefly. There is no reason to go into the details on a job application of your leaving a position.
If a job application asks for a reason for leaving, it is best not to lie. However, a vague answer such as "personal reasons" can be acceptable.
Educational reasons
You could list it as personal reasons.
Looking for a shorter commute.
To write an application of leave for a personal reason one must include when the plan on leaving and how long they would like to leave. They must also include details the are comfortable with providing.
Not drawing a salary. I need a good reason to put on application that will not scare off the hiring person.
Simply list them as "current employer" and the reason for not working. i.e., layoff, reduced hours, etc
You need to put on the application that you left job to be at home with your children. No employer would down upon this.
If you do not wish to answer honestly, then say something like "you wanted to develop your career and felt the change of job was necessary to your developmental experience".
Mutual assistance.
You do not need to disclose your personal reasons for relocating. Just indicate on the job application that you left a former employer due to relocation.