The relationship is often used to describe classifications or groupings. For example, in a geography schema that has the tables Region, State, and City, there are many states that are in a given region, but no states are in two regions. Similarly for cities, a city is in only one state (cities that have the same name but are in more than one state must be handled slightly differently). Each city exists in exactly one state, but a state may have many cities, hence the term many-to-one.
The different elements, or levels, of a hierarchy must have many-to-one relationships between children and parent levels, regardless of whether the hierarchy is physically represented in a star, snowflake, or starflake schema. The data must abide by these relationships. The clean data that is required to enforce the many-to-one relationships is an important characteristic of a dimensional schema. Furthermore, these relationships make it possible to create cubes out of the relational data.
When you define a dimensional model, the many-to-one relationships that define the hierarchy become levels in a dimension.