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The Solar System consists of the Sun, and everything bound to it by gravity. This includes the 8 planets and their moons, the asteroids, the dwarf planets, all the Kuiper belt objects, the meteoroids, comets and interplanetary dust. Since the gravitational effects of the Sun are thought to reach out almost 2 light-years away almost half the distance to the next star there could be any number of objects out there, as part of the Solar System.
There are separate regions in the Solar System. First, there's the Sun, of course. Then there are the inner terrestrial planets: Mercury, Venus, Earth, and Mars. Then comes the asteroid belt; although, not all the asteroids are located in this region. The largest dwarf planet, Ceres, is located in the asteroid belt. Then come the outer gas giants: Jupiter, Saturn, Uranus, and Neptune. Then comes the Kuiper Belt, which includes 3 more dwarf planets: Pluto, Makemake, and Eris. Beyond the Kuiper Belt is thought to be the Oort Cloud, which could extend out to a distance of 100,000 astronomical units (1 AU is the distance from the Sun to the Earth).
Between the planets are smaller objects which never formed a planet or moon. This can range from microscopic dust, up to asteroids hundreds of kilometers across. Beyond the orbit of Neptune, much of this material is icy. The solar wind emanating from the Sun blasts through the Solar System, interacting with the planets, and pushing material out into interstellar space. The region where this solar wind blows is called the heliosphere, and where it stops is called the heliopause.
The immediate neighborhood around the Solar System is known as the Local Interstellar Cloud. It has high-temperature plasma that suggests that there were nearby supernovae. The closest star to the Solar System is the triple star system Alpha Centauri.
The basic informations
Our Solar System was formed when a vast cloud of cold gas and dust was bumped by a nearby supernova blast. The cloud collapsed down and began to spin because of the conservation of momentum of the material in the cloud. The material flattened out into a spinning disk with the middle part becoming the Sun, and clumps in the disk becoming planets.
The Sun formed out of the largest collection of mass at the center of the solar nebula. Because it was spinning quickly, the rest of the nebula collected into a flattened disk around the newborn Sun astronomers call this an accretion disk. Within the accretion disk, additional clumps gathered together; these would eventually form the planets.
The planets started out as tiny specks of dust that clumped together. As they continued to gather together, they became pebbles, rocks, boulders and eventually planetoids. These planetoids violently collided together to become the planets we know today. By studying the decay of radioactive elements in meteorites, astronomers have been able to determine that the Solar System formed about 4.6 billion years ago.
If you define the Solar System as the orbit of the most distant planet, that would be Neptune (sorry, Pluto's not a planet any more). Neptune's furthest point in its orbit is 4.5 billion km, or 30 astronomical units (1 AU is the average distance from the Earth to the Sun). The heliosphere is the point at which the Sun's solar wind is stopped by the interstellar wind within the Milky Way. This point happens at about 90 AU from the Sun. If you define the Solar System as the orbit of the furthest object ever detected, that would be Sedna, which can orbit out to a distance of 975 astronomical units.
Astronomers theorize that a cloud of comets called the Oort Cloud surrounds the Sun out to a distance of 50,000-100,000 astronomical units. This is about 1/3rd the distance to the closest star. So perhaps this is the diameter of the Solar System. Finally, astronomers think that the gravitational influence of the Sun extends out to a distance of roughly 2 light years, which is about halfway from here to Alpha Centauri. So this would be the largest possible diameter of the Solar System.