Cosmic inflation is a proposed period, lasting a minuscule fraction of a second right after the Big Bang, during which the universe expanded exponentially, growing by a factor of trillions upon trillions almost instantly. It was put forward in the early 1980s to solve several puzzles that the plain Big Bang model on its own could not explain.
One of those puzzles was why the universe looks so uniform in every direction, even in regions that, without inflation, would never have had time to interact and reach the same temperature. Inflation solves this by stretching a tiny, uniform patch to enormous size, smoothing everything out before gravity and other forces had a chance to create large differences.
Inflation also predicts that tiny quantum fluctuations present in that first instant would get stretched to cosmic scales, becoming the seeds for all future structure. Those predicted patterns closely match what is actually observed in the Cosmic Microwave Background, which is the strongest evidence in favor of inflation having happened.