Big Bang Theory
The Big Bang theory is the scientific explanation that the universe began about 13.8 billion years ago in a hot, dense state and has expanded ever since.
Definition
The Big Bang theory says the universe began about $13.8$ billion years ago as something extremely hot and dense, and has been expanding and cooling ever since, with stars and galaxies forming as it cooled. It rests on three main lines of evidence: distant galaxies moving away from us (redshift), the cosmic microwave background radiation, and the observed amounts of hydrogen and helium. In its full form, the theory describes the universe evolving under the Friedmann equations of general relativity, predicting Hubble's law $v = H_0 d$, a blackbody background at $T \approx 2.725\ \text{K}$, and Big Bang nucleosynthesis that fixes the primordial helium mass fraction near $25\%$. It does not describe a point in preexisting space; the expansion applies to space itself.
Example
Picture a balloon with dots on it: as it inflates, every dot moves away from every other dot, just as galaxies move apart. In 1929 Edwin Hubble measured that almost every galaxy is redshifted, with more distant galaxies receding faster, and running that motion backward points to a time when everything was together. Nucleosynthesis calculations show that in the first few minutes, at temperatures near $10^9\ \text{K}$, protons and neutrons fused into deuterium, helium-3, helium-4, and traces of lithium, and the abundances measured in old, metal-poor stars match those predictions.
Key Insight
The Big Bang was not an explosion in space like a firework; it was space itself starting to stretch, everywhere at once. A scientific theory is not a guess: this one predicted leftover heat from the early universe before that heat was measured, which is why scientists accept it. The theory describes the universe from a fraction of a second onward, and what happened at $t = 0$, or whether that question even has meaning, lies beyond current physics because general relativity and quantum mechanics have not yet been unified.