Generally people just want to get high enough to get a clear line to the sound sources, and secondarily avoid the chatter if that's a problem. There is also the sightlines of audience members behind the stand to consider. Those are the major concerns. Other more arcane things do come into play though. Here's a few that immediately come to mind:
Anything near the mics can reflect sound. A balcony lip, a celing fan, a big chandalier, a beam, the ceiling itself. It may not make any difference, but sometimes it does. Generally, getting farther away from other things that reflect the sound is better.
Some sound systems are more directional in the vertical plane than others. Sometimes the sound changes dramatically as you move much higher than head height. Since the sound is mixed to sound good down where peoples ears are, it could sound compromised higher up if the sound system's off-axis response isn't even, and many aren't by design.
There is a shelf-type response gain at low frequencies due to reflection off the plane of the floor. The corner frequency of that shelf response is determined by how high the microphones are above the floor. Basically that means more bass when the mics are lower, less if they are higher, all other things being equal. Same can go for proximity to a rigid ceiling.
[edit- here's another]
If you are recording acoustic music, the sound timbre can vary with mic height due to the radiation patterns of the instruments. For example, violins and pianos without lids sound brighter from above. If you are recording a large acoustic source like a symphony, the height of the microphones also effects the spatial depth in the recording and the balance between the musicians in front and those in back, because the distance to each musician becomes more similar as the mics are raised.