Several answers have been given, directly answering the question. Taking a different tack, I'd like to give an answer regarding why the term "falsifiable" is considered so important to science.
Science is founded on the idea of gathering data and analyzing it to produce results. Frankly, both of these cost money (time and effort). Falsifiable claims about the past produce new potential data to gather and new analyses which could provide refutation of the theory. Science may not be able to prove that dinosaurs existed millions of years ago, but they can use that claim to predict which centimeter thick layer of sediment will contain which fossils. If fossils appeared outside of this layer, science has to admit that their theory is falsified, and develop a new falsifiable theory. Creationists lean on this often (geology is not as exact as science wishes it is), discrediting all of science with unusual cases. Whether this is a correct position, or even merely a valid position is outside of the scope of this answer. The important part is that science is falsifiable.
Creationism, however, is typically not falsifiable. It does not matter how much evidence science brings against it, all that evidence is rejected with either "your measuring devices are flawed," or "God built the world in a way which fools science." If one has a faith reason to believe in creationism, no amount of evidence can move that (up until the point where it causes one to question one's faith). When the crux of your argument is "I have a book containing the truth, and it says the past occurred this way," no amount of evidence short of a complete refutation of the book will suffice.
Bringing it back around to cost, the issue that arises is when scientists wish to expends large amount of money doing an experiment. Consider the LHC, coming in at somewhere over 10 billion dollars. This kind of expenditure is not easy to stomach. We, as a society, have to put a lot of faith in science to put that many dollars towards accelerating tiny particles we have never seen before, smashing them together to make even tinier particles that science claims may exist. If a non-falsifiable model of the universe becomes the primary model of how we view things, such expenditures are called into question. "How can we spend so many dollars on science, if the best models they can give us overestimate the age of the Earth by more than a factor of a million?" That doubt will overshadow everything science has given us (including the transistors that let me type this and send it out to the world at a good portion of the speed of light!)
It is possible science will find sufficient new evidence to warrant the development of a scientifically falsifiable young-earth model, but even if that happens, it will not be creationism, because science will never allow a faith based model which cannot be falsified into its canon. Doing so prevents science from improving its models from the collection of new data. There may be a very similar model, maybe even a model that is consistent with creationism, but it will fundamentally be a different model which does not use the Bible as a source of truth information.