A brief account of how the company began- You should mention in your business plan the history behind the formation of you company and the background of the founders and directors.
The primary difference between profit and non-profit organizations is that "for-profit" organizations look to maximize wealth versus non-profit organizations, which look to provide a greater good to society. In non-profit organizations, creative tensions may develop in the effort to balance mission with "margin" (or revenue).
Finally, a business plan should be error - free. This is important because your business plan defines who you are as a business person. If it turned out sloppy, then that does not speak too highly of you.
It also needs to be written in formal format and style. You have to remember that a business plan is something that you may have to present to your business partners, financial firms and banks. So if you can, refrain from using slang in any part of your plan.