What Claire said.
The idea is that if you have enough planets in one Quality (Cardinal, Common, Fixed) or one Element (Fire, Water, Air, Earth) then that quality or element becomes "heavy enough" to give the personality a definite lean in that direction and the characteristics of the quality or element become predominant in the expression of the personality.....the Q or E "outweighs" the others so that it creates an imbalance, which is at the same time a personal strength and weakness.
A preponderance can occur not only in Quality and Element, but also in such things as houses (by cross or triad), aspect type, retrogradation, positive/negative signs, and really any other thing that can be quantitatively assessed.
My own chart is a good example chart for preponderance, because I have several different kinds of preponderance.
7 planets are in Fixed signs. I am incredibly stubborn. Fixed signs are about much more than being stubborn, but that is one of their traits. The Qualities show basically how a person meets and deals with the external world. Fixed signs are something like a boulder in the middle of a stream: the water (passing circumstances) flows around them while they remain unmoved.
5 planets are in Air. This is an Airy preponderance. The Elements are basically subjective/internal and have to do with what I will call perspective or orientation, to how we see and process what we meet in life. We can call Air "mental". Air signs use mental constructs (ideational, theoretical, relational, impersonal and objective) as their way of perceiving and assimilating the world. Again, there is much more to Air than I have described here.
7 planets are in "Water" houses -- the three houses forming a triangle with its apex or point of origin in the Fourth (4, 8, 12). In HIndu astrology these are known as the moksha houses, indicate a good deal of turmoil, suffering, loss and so on with a strongly spiritual orientation to life (because the outer life is so full of disappointments....)
7 planets in Suceedent houses. These houses tend to concentrate and consolidate what is met in life, to build the various experiences of life into some sort of form or structure. They expand and focalize, and their mode of action is to hold fast (something like the Fixed signs).
The combination of "water" houses and "succedent" houses puts a focus on the 8th house. So, 8th house matters and affairs are focalized in this life.
4 planets are retrograde. This shows a very strongly introverted and instrospective personality. Highly subjective, with many setbacks and frustrations probable in the outer world. When General Forrest said "Get there firstust with the mostust", this is the guy who gets there "lastust with the leastust." So then he sits on a stump and tries to figger out what went wrong.....kinda.
7 squares, which is half-again as many as any other type of aspect. (It is the "half-again" that makes an aspect preponderant). The square says you must give things concrete form, bring them to real and substantial existence. It is the aspect of crisis, obstacle, resistance, confrontation, powerful tension. It is the most active and dynamic of the aspects. "Get 'er done."
Many charts have few or no preponderances. My chart is full of them. This just says "This guy has very powerful inclinations to act this way or that way, as a matter of natural tendency." Charts without strong preponderance are more flexible. versatile, adapatable.... Such charts tend to be a little harder to read because they have no definite or clear "leaning" -- or handle to grab them by. Every single detail of a chart holds significance for the life. It is up to the astrologer to find and understand that significance, and interpret it fot the client.
Looking at the preponderances in my chart, it should be obvious that we can learn a great deal about a person by looking at the preponderances (of course, learning what they mean, in depth). Without ever mentioning a single planet in the preceding outlines of my preponderances, you already have a good picture of the life and where it will go.
Peponderance is stronger than any single planet or aspect, because it involves a weighting by ALL the planets, and deals with the chart -- and the person -- as a whole. It is one of the first things the astrologer looks at. Preponderances are foundational to the personality and have to do with how the person orders himself -- his inner structure and orientation in life.
There are also "negative preponderances" (for example, I have no planet in a Water sign). These are just as important as the positive preponderances. Here is where the person "feels a lack" (consciously or unconsciously) and usually there is some compensatory action, an attempt to fill the emptiness.
Preponderance can be gauged by relative strength. For example, in retrogradation it is the common or normal state to see one or two planets Rx. Slightly less common, but still within "expected" limits is three planets Rx. To have 4 Rx planets, or all planets Direct (a negative preponderane) is uncommon. With 5 or more planets Rx we enter the realm of the rare or exceptional.
When something (anything) is either rare or very uncommon, it means that the traits it represents are an outstanding and therefore powerful feature of the personality. We should give these things attention in our interpretation, because they are strong influences in the life.
Mercury is Rx in about 20% of all horoscopes. This then is "uncommon". Mars and Venus are Rx in only about 8% of all horoscopes. This is rare, and always demands special attention.
If we, as interpreters of horoscopes, pay attention to this sort of thing, we find that the horoscope itself shows us how to go about reading it. If we notice something uncommon or rare, our own attention should go there -- because the attention of the native goes there. Whatever stands out in the chart for some reason also stands out in the life, and the attention of the native is necessarily focused there. It shows an individual trait that "stands out."