A very oversimplified description - it's an abbreviation for balanced to unbalanced. What we are talking about here is a device that takes the balanced load (as represented by your loop, which can have 2 wires coming out of it that are identical to each other) and transforms it to an unbalanced load, as represented by the little SMA connector that is found on most RTL-SDR type sticks.
If we don't use a balun, very little energy will flow from the loop to the stick. The problem is that loops like this little AN-200 aren't made to work on a SDR - they are usually intended to work near a portable radio (where it would inductively couple to the ferrite loopstick in the radio) or on a stereo receiver (where the 2 wires would connect to a balun, and then to the stereo itself). There are several different kinds of baluns - one of the more common ones is the so-called 9:1 transformer, often referred to as a 'magnetic longwire balun'. However in this case we need something a bit higher in the ratio. I am just not sure how high you would need to go to accomplish this. I've seen YouTube videos on folks using such a setup (so it can be done), but I am not entirely sure how.
I need to press you on the EXACT model of your SDR. There are some models that would not need a balun for the loop to work properly - the SDRPlay version 2 is one, and I have heard that there is at least one model with an upconverter that might not need it at all. I don't have any idea why you can't or won't say which one it is, because it's tough shooting in the dark without complete information...Mike