If you've studied quantum field theory in any depth you'll have probably come across the idea of a Planck time (sometimes called a planck second). It's 5.4 x 10^-44 seconds and it's a very interesting chunk of time because it's the point at which our laws of physics break down. By that what I mean (roughly) is that if you take Gravity, the energy per frequency of the Universe and the Universal speed limit, it is possible to juggle the terms around so that you end up with a very small distance called the Planck length (1.6 x 10^-36 meters). This length is a mysterious value and we can calculate the amount of time it would take for the fastest thing in the Universe (light) to cross it, giving us the Planck time.
The question really is, where does this number come from and does it have any significance. Here's what we know for definite. The laws of Physics including General Relativity and Quantum Field Theory (the two main branches of what I like to think of as "deep Physics") definitely work on lengths greater than the PL and on timescales longer than the PT. And that's about as much as I can honestly say.
When we drop below these values and talk about shorter distances and shorter times it isn't actually clear that the normal rules of Physics apply. The Planck scales represent the current limit of our understanding so it's very hard to speculate about what goes on beyond them. Some have suggested that these numbers are arbitrary; that they simply appear without any meaning. As if we took the mass of the Pacific Ocean and divideed it by the mass of the Atlantic and called the answer "The Ocean constant". It would be a definit answer, but it might be physically meaningless. Likewise the equation which gives us the Planck units might just be humans putting the main constants together and going voila, there's a number that unifies everything.
On the other hand it's possible that this number really does mean something, making it a fundamental property of the Universe that events cannot happen under the PT and objects separated by less than the PL are indistinguishable. It's possible that time is granular, just like distance. We know that energy only exchanges/exists in discrete chunks so we have to take the possibility that time and space could be the same extremely seriously. But, until we have a working theory of quantum gravity, we just don't know if the laws of Physics stop at the Planck scale, or whether they carry on and we'd just made these numbers up!