I've worked as a BA at a few places...each place had a different idea of what a BA did or should do. I got a degree in CIS focused in systems analysis (I now work as a systems analyst) but did not have my degree before landing my first BA gig.
Most places a business analyst looks at the workflow process and comes up with solutions to increase their ROI.. to over generalize.
I'll enter a business and go over their entire process and come up with ideas to use technology to cut down on man hours so they can focus their efforts in other areas - freeing up time to be used on something else thats more productive.. essentially giving the ability to increase the amount of sales / service they can provide without increasing man power.
There are a lot of businesses out there where I can come up with a solution that will cost them xx,xxx to implement but saves them from hiring another employee at 30-40,000 a year, and also increasing total throughput.
You need to understand both the business and technology side.. most business men don't understand tech, and most tech people just don't understand business