How was the Big Bang different from an ordinary explosion? Where in the universe did it occur?

The Big Bang Theory stands among the most significant scientific explanations regarding the origin and evolution of our universe. At its core, it is a cosmological model that describes how the universe expanded from a very high-density and high-temperature state.

Contrary to popular imagery, it wasn't an 'explosion' in the traditional sense, with fragments flying out into empty space. Instead, the model delineates a process in which spacetime itself began to stretch and expand. According to this model, this incredibly hot and dense point, also known as a singularity, marked the commencement of the universe approximately 13.8 billion years ago.

The Big Bang Theory not only gives us a starting point for the universe's history but also serves as a foundational framework that integrates various strands of astronomical observations and physics, including the cosmic microwave background radiation, the abundance of light elements, and the Hubble Law pertaining to the motion of galaxies.

One of the foremost predictions of the Big Bang Theory is the continuous expansion of the universe. But what does this actually mean? Rather than a central explosion flinging material into empty space, spacetime itself is expanding, and as a result, galaxies are moving away from each other.

This observation was first made by Edwin Hubble in 1929 and is now famously known as Hubble's Law: the farther away a galaxy is, the faster it appears to be moving away from us. This expansion is often visualized as dots on a balloon that gets bigger; as the balloon inflates, the dots move farther apart, not because they're moving on their own, but because the surface of the balloon is expanding.

This discovery was monumental, leading to the inference that the universe must have been denser and smaller in the past. In essence, this expansion of the universe serves as one of the most compelling pieces of evidence for the Big Bang Theory.

At the center of the Big Bang Theory lies the concept of the singularity. A singularity in astrophysics is a point in spacetime at which density and temperature become infinite. The laws of physics as we know them breakdown at this point and it becomes a position of 'infinite density'. This theoretical point is not a location within the universe but rather represents a moment in time — the very instant of the universe's formation.

While it provides the starting mark for the universe's existence, singularities pose profound questions, especially since the rules of conventional physics cannot yet describe those conditions adequately. This is where quantum mechanics and general relativity collide, and where current research in theoretical physics, including string theory and the search for a unified theory of quantum gravity, are chasing answers to deepen our understanding of the universe's origins.