Proliferation is a rapid multiplication of parts or the increase in the number of something. Nuclear proliferation is a rapid increase of nuclear weapons.
The proliferation of any living thing will often create an overpopulation problem and cause an environmental imbalance. A proliferation of fuzzy koala bears might seem kind of nice, but these cute little creatures would soon eat up all the eucalyptus, running out of food and causing problems for other species. We almost always use this word to describe stuff we don't want to increase rapidly. The excessive proliferation of mutated cells, for instance, is how cancer grows.