The theory of cosmic inflation was developed in the early 1980s to try to explain what happened to the universe directly after the Big Bang. For a long time, scientists had a difficult time explaining some characteristics of the universe: for instance, its flatness and its fairly even temperature. Something must have happened, they decided, to allow these characteristics to come into being.
Alan Guth came up with an idea about what that something might have been. He proposed that for a short time after the Big Bang, the universe expanded very, very quickly—as in exponentially quickly. This took place in a mere moment, and during that moment, the universe essentially blew up like a balloon because of the presence of a massive amount of vacuum energy in the universe.
As that vacuum energy depleted, inflation slowed down and actually decayed, transforming into radiation and matter, which scattered throughout the universe in a particular pattern. This pattern created variations in density that allowed for the development of the elements of the universe.
We can see, then, that during inflation itself, the universe was characterized primarily by an extremely rapid expansion due to the presence of vacuum energy. As inflation slowed and faded, it left behind many of the characteristics scientists still observe in the universe as well as the building blocks for further development.