the easiest way to understand it it this - the goal of partioning (whether manual or automatic) is always and always to strike a balance between query response time and cube build time. Smaller the partition, quicker the query response (because it has to scan smaller partitions) but longer the cube build time. Now, this is where you need to strike the balance - you don't want a very quick cube build but very long query response time, nor do you want a quick query response but a large cube build time.
so what does partitioning really do? Partitioning will presummarize the data in the PowerCube and store it into partitions for quicker retrieval. If a cube is very large and doesn't have these partitions, user response time will be slow. But a cube with a large number of these partitions will just increase the build time.
partitioning performs well when the number of categories and their children are limited in that a few at the top level with a few hundred at the child level. But, if the top level itself contains a few hundred categories with tens of thousands in the level below it then partioning will not work well.
you can play around with the numbers on the auto partition tab of the powercube properties. Build the cube once with default settings and then look in the log file. Get the end count consolidation off it and put that in the estimated number of consolidation records in the tab. Change some of the other settings and build the cube a few times. The key, for each cube build, is to check the log file and compare the "Performing Pass 0" numbers and the Last Pass (Pass 6, 7 etc...whatever is the last pass number) numbers and ensure that the row count of the 0th pass is less than the row count of the last pass. Additionally, the category count of the last pass should be lesser than the 0th pass (although may not be significantly less)
You can also opt to choose manual partitioning but that is a can of worms you may want to avoid unless you know your data inside out (how many categories in each dimension, how are they expected to change over time etc. )and are prepared to spend a lot of time with trial and error to find out the best strategy