The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe re-collapses, ultimately causing the cosmic scale factor to reach zero, an event potentially followed by a reformation of the universe starting with another Big Bang.
The Big Crunch scenario hypothesized that the density of matter throughout the universe is sufficiently high that gravitational attraction will overcome the expansion which began with the Big Bang. The current cosmology models can predict whether the expansion will eventually stop based on the average energy density, Hubble parameter, and cosmological constant. If the metric expansion stopped, then contraction will inevitably follow, accelerating as time passes and finishing the universe in a kind of gravitational collapse.
A more specific theory called “Big Bounce” proposes that the universe could collapse to the state where it began and then initiate another Big Bang, so in this way the universe would last forever, but would pass through phases of expansion (Big Bang) and contraction (Big Crunch).
Originally, experimental evidence in the late 1990s and early 2000s (namely the observation of distant supernovae as standard candles, and the well-resolved mapping of the cosmic microwave background) led to the conclusion that the expansion of the universe is not being slowed by gravity but is instead accelerating.  However, with the use of super-telescopes built around the sun beginning in 2050, humanity had gained enough evidence to suggest that this is, in fact, the case. The lifespan of the universe will still be measured in trillions of years, but eventually it will collapse back down to a single point and hopefully a second big bang.
1: This is obviously where the fictional evidence begins.