A Bill of Materials (BOM), is essentially a list of products that are required to produce another product. You can think of it like the list of ingredients for a recipe. Odoo needs to know what materials are required for us to produce this Class of 2017 T-shirt product.
In complex products, a bill of materials can be nested. For example, it may take many products to make a sub-product, and then several sub-products to make a final product.