Sql Server Analysis Services, a powerful tool, large in scope, deep in subject.  You could literally write books on SSAS, and they have, but what is it's use?  Well, Business Intelligence is the first obvious answer, but BI can be delivered from just SSRS (SQL Server Reporting Services).   What is a report though? A report is generally speaking a predefined view of data that allows a user to get the values they want to see from a set of data.

SSAS delivers the same concept, plus other data that the user hasn't even requested yet, but, as we all know, they'll ask for it tomorrow.  Today the user is happy with seeing total sales for a particular week, itemized by stores.  However tomorrow they want to see sales for the week, itemized by category instead of stores.   Can you deliver this in SSRS? Sure you can...lets work up a new query and a new report.... but how would SSAS potentially make this easier/faster?

SSAS can bind to SSRS, or other third party reporting tools, but where it really shines, IMO, is it's "auto-magic" functionality in Excel.  As can be seen in the picture below, in 2007/2010, if you open a sheet, you can click on the Data tab, then choose "From Other Sources" and then use the option "From Analysis Services".

Naturally you'll need access to an SSAS cube that has been created already, but excel will let you work with this cube in a drag and drop style environment.  A pivot table is setup for you and calculations generated based off the columns, rows, and numbers(measures) you drag into the fields to see.  Automatically allowing on the fly filtering from drag-drop menus, filters, or if you have 2010, you can use Slicers.  Slicers being basically windows with filter options letting you quickly select multiple values to aggregate data by.

So think about it like this, with SSRS only, you could get a request for a report that you can deliver in a few hours.  With SSAS, and just Excel, that request could be avoided completely, the end-user could just drag-drop the values they want to see on a pivot table and see the numbers immediately.   Allowing them to play around and see some numbers that aren't really critical enough to actual get someone to make a report for.

Also, another handy feature of excel, is the ability to select a pivot table you already created and just spawn a pivot chart from it with a few clicks.  So essentially your spawning sales dashboards in moments, instead of hours.  And again your trashing sales dashboards you don't like because the overhead cost to make them was so tiny why not create a few and throw them away? It's not like someone slaved for hours to make a pretty pie chart or bar chart, you did it in seconds with a couple mouse clicks.

All of this of course depends on someone setting up SSAS, getting the cube built, dimensions, proper measures, and applicable permissions.  Again a very broad subject, and this blog post still probably doesn't hit the general concept well enough, but the key is to understand that SSAS is very powerful in Business Intelligence, and if leveraged correctly can save lots of time in end-user data analysis.