Our solar system formed from the force of an exploding star. When some stars reach the end of their lives, they can explode into a supernova, sending shockwaves of energy deep into space. Roughly 4.5 billion years ago, a shock-wave from a supernova, travelling at 30 million kilometres (19 million miles) per hour, hit a cloud of ice, dust and gas. The force of the impact caused the cloud to flatten and rotate. From this spinning disc, our Solar System began to form.
The most widely accepted scientific explanation for the formation of the Solar System is called the Solar Nebular Model. According to this model, the entire Solar System formed around 4.5 billion years ago from the gravitational collapse of a small fraction of a giant molecular cloud, also known as a nebula.
A disturbance, most likely a nearby supernova, caused a giant cloud of gas and dust floating in space to contract and begin to collapse on itself. Most of the gas collected in the center to form a gaseous sphere that would eventually become the Sun. As more gas was drawn inward by the force of gravity, friction and pressure caused this sphere, called a protostar, to become hot and start to glow.
As the nebula continued to contract, conservation of angular momentum caused it to spin faster. It flattened out into a protoplanetary disk, with the hot, dense protostar in the center. Over millions of years, all eight planets formed by accretion from this disk. In other words, gravity pulled the disk into many clumps of gas and dust. These clumps stuck together and grew larger and larger, turning into planetesimals. The planetesimals further coalesced to eventually form planets, with comets and asteroids being the leftovers. Gravitational interaction with the planets caused them to be grouped into distinct regions such as the asteroid belt and Kuiper belt.
Due to their higher boiling points only metals and silicates could exist in the warm inner solar system, and these would form the rocky planets of Mercury, Venus, Earth, and Mars. Since metallic elements only comprised a very small fraction of the solar nebula, the terrestrial planets could not grow very large. It is thought that as many as 100 small protoplanets used to exist in the inner solar system, but they eventually collided and merged to create the four inner planets we know today.
The gas giants (Jupiter, Saturn, Uranus, and Neptune) formed further out, beyond the frost line where icy compounds can remain solid. The gas and ice that formed the Jovian planets was more abundant within the protoplanetary disk, allowing them to become massive enough to gain large atmospheres of hydrogen and helium and grow to mammoth proportions. Uranus and Neptune are thought to have formed closer to the Sun, and then migrated out to their current orbits.
Throughout all this, the infant Sun continued to grow hotter. Once the temperature and pressure at the core was high enough, thermonuclear fusion of hydrogen began, and the Sun became a fully-fledged main-sequence star. Solar wind swept away the remaining gas and dust leftover from the protoplanetary disk into interstellar space, ending the growth of the planets. This entire process of solar system formation happened within several hundred million years and was finished by around 4.5 billion years ago.