I've seen on large sump systems at a pet store, that there is a line for minimum and maximum water levels. Out of curiosity what happens if the water goes below or above those lines?

I think the lines just represent where the systems performs like it is supposed to. Water flows through the filtration properly and nothing is by-passed.

If the overflow or the inlet to the sump clogs, water will drop below the minimum line in the sump and hopefully you have a float gauge that will kill the pump before it burns up, and the water level is hopefully low enough in the tank or the pinhole in the inlet succeeds in breaking the siphon or emptying the sump before the tank overflows. If the outlet clogs or the pump fails hopefully the pinhole in the inlet breaks the siphon before the sump overflows.

My speculations - I don't actually run a sump.

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