It means that it is impossible for the viewer to figure out the order of the exhibit. The exhibit is so mixed together that it is hard to make a connection from piece to piece to figure out an order.

"The exhibit is arranged in no important order that the viewer can discern"? A synonym for DISCERN here would be "FIGURE OUT" or "TELL" [ "TELL" in the sense of "I can't tell what's going on" or "I can't tell what she is thinking" ] So, your sentence means... It's hard to tell (discern, figure out) if this exhibit has an organization or structure. The exhibit doesn't seem to be in any discernible (adj) order. I can't figure out (discern) what the system is for this exhibit, or if there even *is* a system. I'm sure you're aware of this, but just to clarify the context -- it's my experience that exhibits have a number system, and similar exhibitors are grouped together so people can make sense out what's going on. For your sentence, it sounds like the exhibit is random -- there is no system or organization -- or, if there is a system, the speaker/writer can't figure out what it is.

To discern can mean to figure out or work out something, for example, to explain why something has been done in a certain way. It can also mean that someone is a discerning person, to say they have high standards for things, for example, this antique is in good condition and has good provenance and would therefore be of interest to a discerning buyer. I'm not a teacher nor even an expert in my own language but I hope it helps you.