Cosmic inflation is the idea, first proposed by Alan Guth in 1981, that the infant universe passed through a phase of exponential growth. The expansion was driven by a negative pressure vacuum energy density. This expansion is similar to a de Sitter Universe with positive cosmological constant.
As a direct consequence of this expansion, all of the observable universe originated in a small region that was causally connected - meaning that all regions could exchange information at spatial speeds less than the speed of light. It means that the temperature could even out over the whole region.
This is not the case with the Friedmann universe, where the expansion rate approaches infinity at time zero. Different regions of the embryonic universe were moving apart so fast that light could not move between them.
Note: space can expand faster than the speed of light. It is only moving through space that is restricted to the universal speed limit.
Quantum fluctuations in this microscopic region, magnified to cosmic size, then became the seeds for the growth of structure in the universe.
The name of the theory was a semi-humorous reference to the economic inflation in the USA in the late 1970s.