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While ROS is used in many research laboratories and universities, you don't have to be an academic to use it.
I would say as a general guide, you will want to have some background in the following.
If you have some basic working knowledge of these things, then you should have no trouble using ROS. Some of the higher level concepts are more mathematically rigorous (or rely more heavily on computer science and control systems knowledge), but most of these things can be learned from Wikipedia or other sources of information on the web. I am currently mentoring a group of undergraduates on a robotics project, and they have had no trouble attaining the skills necessary to work in ROS.