Definition of inflation:

Inflation is defined as the period when the scale factor, a(t), which is a measure of the size of space, grew exponentially with time. The scale factor may have changed by about 60 e-foldings.

Inflation is currently the mostly widely agreed upon model that describe the dynamics of the early universe. It is, however, somewhat controversial because the physics required for such a scenario are somewhat exotic. The theory posits that the decay of a scalar field, and the associated particle; the inflaton, is responsible for fueling the massive expansion.
Although neither the inflaton nor any scalar fields have ever been found, inflation is still very compelling because is passes some key tests.