In the most basic sense, a business model is the method of doing business by which a company can sustain itself -- that is, generate revenue. The business model spells out how a company makes money by specifying where it is positioned in the value chain.
That's related to a business plan like an idea or plot summary is related to a novel. A business plan sets forth what a company intends to do in the future, usually in detailed steps summarizing objectives, market, products, strategy, management team, and financial projections. You can see hundreds of examples of business plans, and read more about them, on Bplans.