I am going to simplify and try and offer a basic disucssion about "heights" .
I assume that if the user is asking this question then most three syllable meteoroligical terms are not going to help explain things.
In my simple view of things.. "heights" are a way to express air pressure. They provide a clearer picture of what is happening at various levels of the atmosphere. Before we go to far into this I should pause and state that my "breakthrough moment" with going further into understanding meteorology was the hodograph and the SkewT. These are graphs of the change in temp/humidity and wind in the column of air directly above a point. Those made sense to me way before anything else did. I do not know why Meteorology classes do not start with SkewT and move from there.
Anyhow back to heights.
Note that I may be simplifying in a way that offends the experts. If the experts care to clarify or correct then please do.
First we should talk about pressure.
Why does pressure matter. Well if the pressure is low then air at the surface will tend to rise and that leads to storms and that is good. I sometimes oversimplify the details of air pressure and say something like
"High air pressure is falling air and low air pressure is rising air".
The experts can clarify but that often helps folks get a handle on air pressure. Understand that pressure differences are key to defining air movements so we measure air pressure as part of our meteorological data. In addition to air pressure at the surface it is important to track air pressure in the column of air above you. When you track or measure air pressure aloft you have a number of choices as to how to map that information. What probably first comes to mind is that you could say "at an altitude of 10,000 meters over St Louis the air pressure was x, over Kansas City the 10,000 meter air pressure was x, etc etc"
Although measuring Air pressure aloft in the above manner makes sense at first what you end up with is a bunch of data with constant altitude but differing pressures.
Another way to track the same data regarding pressure aloft is to measure the altitude at which the air pressure was 500mb. So we think of the 500mb as the data point that remains constant and now we track at what altitude that occurs. So we map the height of the 500mb "surface". We end up with a "contour map" or "topo map" (in a sense) of the height where the pressure is 500mb. As the pressure changes then the height of that surface changes. Thus we get the term "height falls" .
I hope that hels the OP and any other beginners. I hope I did not offend any technical experts with my simplification. Good books on meteorology seem to be the Ahrens books.
What helped me understand mesoscale events more than any other tool was learning Skewt and hodograph data. This is the picture given from either a weather balloon launched from a point, or a forecast of data that would be gathered from a weather balloon launched from a point. That allowed me to grasp lapse rates, shear and the like and therefore Cape and Cap and all that.
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Tom