One of the most powerful tools in the BI stack is the SSAS cube. The cube is a collection of related dimensions and measures that, once completed, can provide an enormous about of data that can be sliced just about any way you want it... Oh, and it'll do it just as fast as you can click your mouse. Now like I said, within a cube there are dimensions. These are a lot like the ones you'll see in your data warehouse. A lot of times, within dimension, you'll find hierarchies. Hierarchies are logical entities that an end user can use to analyze fact data. These entities can be made of one or multiple levels and can manifest itself in one of three ways: balanced, unbalanced, or ragged.
A balanced hierarchy is one that all of the branches of the hierarchy reach to the same level and each member's parent belongs to the level immediately above it (no gaps in levels). One common example of a balanced hierarchy can be found in a date dimension. Here is an illustration of what I'm talking about:
As you can see, all of the branches reach an equal length and there are no gaps in levels.
The second type of hierarchy is unbalanced. In an unbalanced hierarchy, all of the branches of the hierarchy don't reach to the same level but each member's parent does belong to the level immediately above it. One example of this type of hierarchy is an employee hierarchy. There may be some positions on the same level that don't have direct reports, while others do. Here is an illustration:
The last type of hierarchy is called ragged. In a ragged hierarchy, each level has a consistent meaning from branch to branch, but one or more branches might have a missing level. An example of this may be a geography hierarchy, as seen below.
I hope this sheds some light on the different types of hierarchies you'll be working with on your next SSAS project.