[aroberge]

The big bang hypothesis could be stated (in a simplified way) by stating that the universe was once a lot more hot and dense than it is today. Using General Relativity, we can model the expansion of the universe. When we do the math, we find that out come correctly the relative abundance of light elements in the early universe as well as the spectrum for the cosmic microwave background, and many other quantities. It holds very well together.

If we extrapolate far enough back, we reach a point where the predicted density would be infinite. We call that point the beginning of time (or the big bang). This "prediction" of an infinite density is taken as a sign that our model breaks down at (or before) this point (by "before" I mean when we extrapolate backwards in time towards the infinite density time...).

So, it works extremely well for a time when the density was extremely large (but not infinite) until today. We just don't have enough information to know what would happen when densities larger than a certain value so as to make meaningful predictions.

To make a completely silly analogy: it would be like predicting the motion of a rocket aimed for a comet. Our knowledge of celestial mechanics is good enough to predict the trajectory up until the rocket "touches" the comet. We just do not have enough information about the comet composition to know if the rocket will just blow it apart or if it is the rocket itself that will splatter on the comet, or whatever.