What do these mysterious "Business Intelligence" software do anyway ?
They're not really mysterious. BI or Business Intelligence software is just a term that groups software with a particular goal like OLAP and report generators. SSRS and Crystal Reports are some examples, among many others.
And the requisite wiki article...
In a nutshell, the goal of BI is: aggregating and presenting data to help executive decision making.
In a business, the role of a CEO is to stay on top of pretty much everything that is happening in a company. Some data you can get off of standardized reports, but sometimes you have an intuition, and need to actually dig through the data in arbitrary ways, while not really being able to learn SQL. BI is there to fill that role. It is there to do a better job then the CEO actually exporting a bunch of reports into excel, then massaging the data there.