The term Big Bang often refers to a cosmological event that took place approximately 13.8 billions years ago and the Universe was born as the result.
It was an explosion
Most people imagine the event as an explosion for at least 2 reasons. First is the name it self and secondly, a large number of significant events happened in a very short span of time after the event.
The Universe had a temperature of 10^32 K at 10^-43 second after the event and had 2 forces, Gravitation and Nuclear Strong, Nuclear Weak and Electromagnetic forces combined into one. At 10^-35 second, the Strong interaction separated leaving Weak and Electromagnetic forces as one. This was followed by an accelerated expansion of Universe till 10^-32 second, referred to as “inflation”. Universe expanded by a factor of at least 10^28 in this period and attained the size of grape fruit at the end. This was much faster than the speed of light but did not violate Special Theory of Relativity as this was stretching of space and not movement of a body. The definition of unit of space say meter expanded exponentially. The Universe was also cooling exponentially and by 10^-10 second, Weak and Electromagnetic interaction got separated creating the 4 forces of nature as known today followed by creation of protons and neutrons. The Universe had a radius of 10 light years after 1 sec and not 1 light second.
The continuous fall in temperature allowed nuclei to be formed from around 200 seconds onwards but temperatures have fallen so much that this process stopped in a few minutes. Unaided by Gravity, this temperature of around 10^7 K could not sustain nuclear fusion reactions and humans have experienced the same issue as they try to develop nuclear fusion reactor. At that time, about 3/4th of Universe consisted of Hydrogen by mass and rest was Helium with very minor traces of Lithium. At around 379000 years, atoms started appearing and reduction in ionized particles allowed light to shine through forming Cosmic Microwave Background (CMB) radiation. Light cannot be used to study Universe before that, one hope being to use Gravitational Waves which are being detected frequently.
Thereafter, it took many million years for Gravity to aid formation of stars and galaxies and after a billion year, the appearance of Universe changed little.
It was not an explosion
However, most scientists do not consider Big Bang to be an explosion. First, there is no theory that describes what happened from the event till 10^-43 second, also called Planck time. This theory will merge Quantum Mechanics and General Theory of Relativity. Extrapolation of General Theory of Relativity yields a singularity and the theory is not valid before Planck time.
Most importantly, Big Bang created space and time besides energy and matter. It was not an event that someone could have watched at a distance as there was no space or reference frame outside the Universe. The expansion of Universe created space itself and not expansion into space. It was not like a cracker explosion where matter scatters from a point but was movement of each point relative to every other point.
Observations today
Size
The size of the Universe is independent of the position and direction of observation and yields the same value, i.e. a sphere of radius 46.5 billion light years. This is called Observable Universe. This is fraction of actual Universe which is much bigger, at least 250 times bigger. The stretching of space that started with Big Bang continues though at a slower rate, hence this number is more than the expected 13.8 billion light years. In fact this is used to calculate the age of the Universe, light from galaxies at the edge of the Universe have taken 13.8 billion light years to reach us. In future, light from more galaxies will get time to reach us making them visible but some visible galaxies will start moving faster than speed of light and hence disappear from our view.
Hubble’s law says that all galaxies seem to be moving away from us and each other with speeds increasing with distance. This implies that there is no preferred centre point of the Universe or a place to say where Big Bang took place and is yet another reason not to treat this as explosion but a continuous event.
Inflation
One related question is the shape of the spacetime curvature of the Universe. The curvature of Universe to an 0.4% degree of accuracy is flat, the initial curvature of the Universe was flattened during the inflation period. The flat curvature also implies that the Universe will continue to expand and expansion will stop after an infinite amount of time. The density of Universe matches the critical density needed for the flat curvature. Also even now, about 3/4th of Universe consists of Hydrogen by mass and 1/4th is Helium if Dark matter is excluded which is very difficult to detect.
The inflation also explains the homogeneity of CMB, its uniform temperature in whatever direction the measurement is taken, including between distances that light could not have travelled since the birth of the Universe. The expansion of Universe transferred uniformity even between bodies not in causal contact now but causally connected at that time. Even in this sea of homogeneity, some quantum fluctuations induced patches of lumpiness resulting in formation of galaxies.
Many scientists consider the inflation to be the real “Bang” due to the enormity of the event and sometimes one hears the word “Big Stretch” rather than Big Bang.
Conservation Laws
The Universe is homogeneous, i.e. all points in the space are same and hence laws of Physics do not depend upon where we chose our reference frame to be. This translates into Law of conservation of linear momentum. Similarly, Universe is isotropic, i.e. space has same properties in all directions and hence laws of Physics do not depend upon orientation of coordinate system. This translates into Law of conservation of angular momentum. The fact that the laws of Physics do not depend upon what we choose t=0 to be results in law of conservation of energy. These and other symmetries of the Universe give arise to conservation laws that govern Physics up till the particle physics level.
Theory
Big Bang created a homogeneous, isotropic, expanding Universe with indefinite life. Nowadays, scientists gave more importance to Big Bang Theory which governs the entire life cycle of the Universe even as the research continues to understand the event it self.