The theological significance of inflationary cosmology is this: It shows how the universe can have formed from nothing, in complete chaos (maximum entropy), and have order form spontaneously, without violating any known principles of physics. That is, it provides an economical explanation of the origin of the universe without creation or design. A creator is not required by the data. In general relativity, space-time can be empty of matter or radiation and still contain energy stored in its curvature. Uncaused, random quantum fluctuations in a flat, empty, featureless space-time can produce local regions with positive or negative curvature. This is called the "space-time foam" and the regions are called "bubbles of false vacuum." Wherever the curvature is positive a bubble of false vacuum will, according to Einstein's equations, exponentially inflate. In 10^-42 seconds the bubble will expand to the size of a proton and the energy within will be sufficient to produce all the mass of the universe.
The bubbles start out with no matter, radiation, or force fields and maximum entropy. They contain energy in their curvature, and so are a "false vacuum." As they expand, the energy within increases exponentially. This does not violate energy conservation since the false vacuum has a negative pressure (believe me, this is all follows from the equations that Einstein wrote down in 1916) so the expanding bubble does work on itself.
As the bubble universe expands, a kind of friction occurs in which energy is converted into particles. The temperature then drops and a series of spontaneous symmetry breaking processes occurs, as in a magnet cooled below the Curie point and a essentially random structure of the particles and forces appears. Inflation stops and we move into the more familiar big bang.
The forces and particles that appear are more-or-less random, governed only by symmetry principles (like the conservation principles of energy and momentum) that are also not the product of design but exactly what one has in the absence of design.
The so-called "anthropic coincidences," in which the particles and forces of physics seem to be "fine-tuned" for the production of Carbon-based life are explained by the fact that the spacetime foam has an infinite number of universes popping off, each different. We just happen to be in the one where the forces and particles lent themselves to the generation of carbon and other atoms with the complexity necessary to evolve living and thinking organisms.