Business Processes are the operations that a business goes through to bring you the final product.For eg.Raw Materials -  Transport to Factory -  Processing of Materials -  Bring to Warehouse for Storage -  Distribute to Retail Outlets -  Sales and Marketing -  Post Sales SupportThis whole thing is a business process.Outsourcing means you give another person to take care of a certain part of this whole process. For example you ask another company to do the   Raw Materials -  Transport to Factory -  Processing of Materials -  Bring to Warehouse for Storage  and you pay them for it.
You own a company and it will cost you $100 to make 10 books, that being too much you will outsource that work to me for $50 for the same amount of books with the same quality. So now you save $50 and make the same profit making it more cost effective.
Business process outsourcing is just a term where big companies to sell or improve and provide support for their products , try to outsource to other comapnies, so that they can indirectly help in imporving the business.