The Big Crunch is a theoretical prediction about the end of the universe which was believed for much of the latter half of the twentieth century. In this theory, the universe would eventually stop expanding and collapse back into a "primordial atom" like the one at the start of the universe according to the Big Bang theory.
This theory had a beautiful symmetry to it, which certainly made it appealing to many physicists. Unfortunately, when astrophysicists conducted a careful scientific analysis in 1998 of the astronomical data to detect the deceleration rate of the universe's expansion, they found something quite unexpected. Instead of decelerating, the expansion of the universe was actually accelerating. This research earned these scientists the 2011 Nobel Prize in Physics.
Extensive research since 1998 has continued to provide evidence that the universal expansion rate is accelerating, though the exact force causing this acceleration is unknown. The common name for this unknown force is dark energy, and it is one of the great problems in theoretical physics that is prompting significant research. Until dark energy is more understood, there's no way to rule out the possibility of a Big Crunch, but the theory has largely fallen out of favor.