Cosmic inflation is a well supported theory that states the early universe expanded exponentially resulting in several observable consequences. It is important to define the "early universe," as different branches of physicists and cosmologists will use separate time scales. The age of the universe referred to is fractions of a second old. That is to say less than a second following the big bang. The inflation happened in an extraordinarily short amount of time. The current estimate refers to the "inflationary period" lasting from 10^(-36) seconds to 10^(-33) seconds after the big bang. The universe continued to expand following the inflationary period, however not at exponential rates.
A consequence of the inflationary period that are able to be confirmed is the evidence of a seemingly flat, homogeneous observable universe and one that obeys the cosmological principle. Do not let that jargon confuse you as all it means is that we are not in some special area of the universe when it comes to the laws of nature as we understand them. It is important to note that this makes no assertion on the probability of life, nor that earth is or is not special because of life, only that the physical laws like gravity and electromagnetism are no different here than they are at any spot in the observable universe.
The exponential expansion resulted in a universe growing faster than light can travel. Thus, the inflationary period gives us a distinction between the observable universe and the entire universe. The observable universe is but a fraction of the entire universe and is the part of the universe in which light has had enough time to travel since the beginning of the big bang. This portion of the universe is simply approximated by multiplying the time since the big bang by the speed of light. Because these numbers are so vast we define a distance known as the "light year" which is the distance light travels in a year, or roughly 9.46 × 10^15 meters. Though the size of the observable universe is mind-boggling already, the entire universe may dwarf that number. It is currently impossible to ascertain how large the whole universe is as we cannot see further than light has traveled.
A final consequence of the inflationary period is the problem of the magnetic monopole. Previous to the inflation hypothesis the big bang model hypothesized the existence of an abundance of magnetic monopoles. Current observations were unable to detect such monopoles and thus resulted in an attack on the big bang theory. Inflation predicts a scattering of monopoles such that the density of magnetic monopoles is so small it would be extremely rare to see one. This matched our current view of the universe and solved a very large problem in modern cosmology.