The Wikipedia article on the subject is quite good:
Basically, it's a proposal for the behavior of our early universe, one that has been essentially confirmed by detailed measurements of the cosmic microwave background (though there still remain a couple of other alternative proposals).
The idea goes as so:
During the earliest stages of our universe, it was dominated by a large energy density in a particular field, a field that experienced some potential energy. This field would have been moving towards its minimum potential energy as the universe expanded, but the expansion itself acts as a friction that makes it more difficult to roll down its potential energy towards the minimum. As a result, the energy density of this field was nearly constant with time, a feature which drives an exponential expansion. So while this field dominated the universe, the universe expanded at an exponential pace (and a very fast exponential pace at that: this field had to have had lots of energy). Once the inflaton field reached the minimum of its potential, it started rolling back and forth, and this oscillation caused it to decay into all sorts of other particles, becoming all the stuff we know and love.
More details are at the above link.