The grain (or granularity of the fact) refers to the 'level' at which you're taking a measurement. A fact table describes a measurement taken of a business process, so the best way to describe the grain is to describe what you get for each row. The classic example for a supermarket checkout is 'one row for every beep/scan'. This is better than saying 'one row for every day, product and store' (i.e. naming the dimensions) because it grounds it in reality.
The grain/level element is that you might be storing a row at a level of product, or you might be storing it at some grouping of products. This matters as it will determine whether you can use the product-level dimension or the group-level dimension with it.