If there's a preponderance of something, there is A LOT of it. If you are a prosecutor, you are looking for a preponderance of evidence to convince the jury that the defendant is guilty.
The noun preponderance can also mean "superiority in weight or significance." This meaning is particularly reflective of the word's Latin roots in the word praeponderare, which means "outweigh." The noun can also mean "superiority in influence or importance." A country's economic preponderance, for example, might give it greater influence in international relations.