Definitions for "big bang theory"
The theory that the known universe originated in an explosive event (the big bang) in which all of the matter and energy of the universe was contained in a single point and began to rapidly expand and evolve, starting as high-energy particles and radiation, and, as it cooled over time, evolving into ordinary subatomic particles, atoms, and then stars and galaxies. According to this theory, the four-dimensional space-time continuum which we perceive as our universe continues to expand to the present time, but it is unknown whether the expansion will continue indefinitely or eventually stop or even reverse, possibly leading to a contraction to a single point sometimes referred to as the "big crunch". The competing "Steady-state Theory" gradually lost favor in the 1980's and 1990's. See also big bang.
A theory that says the Universe began with a super-powerful explosion.
The widely held belief that the Universe began in a fiery explosion, 10-15 billion years ago. The cosmic microwave background, big bang nucleosynthesis, and the observed Hubble expansion of the Universe are considered proof of the big bang theory. For more on big bang cosmology, check out this primer.