The solar system is composed of the inner rocky planets (Mercury, Venus, Earth and Mars), beyond which are the gas giants, which probably have solid cores but are essentially big blobs of fluid (gas at very cold temperatures is a fluid).
The reason why silicon is the most common element within the rocky planets, is because it was the most common element (next to hydrogen) in the original nebula that condensed to form the Solar System. This is simply how our Solar System was at the start - it had a greater ratio of silicon to all the other elements except hydrogen. Perhaps other planetary systems around other stars may have more aluminum or iron than silicon. Ours just happened to be a silicon-dominant one.
Within the rocky planets however, although silicon is dominant, there may be smaller variations in the ratio of silicon to other elements. For instance Mercury is thought to have a large iron core with a thinner silicon (rocky) crust (compared to Earth which has a small iron core with a large silicon crust). This may be because heavier elements like iron & nickel were concentrated towards the inner part of the early Solar System when it was still condensing. This is due to gravitational forces - heavier atoms fall towards the centre of the spinning nebula, lighter gases drift towards the perimeter. Another different theory suggests Mercury had part of its silicon crust blasted off by impact with another large planetary body a long time ago.
This has to do with how we believe the solar system formed from a hot mass of swirling gas and dust. Your question can be answered in 2 parts: why there is more iron and silicon in the universe than heavier elements like gold and uranium, and why is the earth mostly made of quartz (silicon dioxide) and iron compounds when hydrogen and helium are the most abundant elements in the universe. So let me go back to how we think the solar system formed...
We have elements in our solar system like iron and silicon because they were formed by earlier generations of stars that blew up as supernovas, and spewing them out into space. In stars, nothing heavier than iron can by made by nuclear fusion, so everything heavier than iron, (like uranium and gold and mercury and osmium) are formed in the supernova explosion itself. Our solar nebula must have been formed from the left-over remains of these earlier generations of very big and hot stars that ended their lives as supernovas.Because large stars have time to fuse heavy elements in their cores, they create everything up to iron, so all those elements like silicon, oxygen, nickel, iron, sulfur, are formed inside the star. Everything heavier can only be formed in a supernova explosion, so that explains why they are much less abundant - they have much less time to form.
Now, hydrogen is the most abundant element in the universe, and helium is second. (These are the lightest elements we know of.) So how come there is not much of them on earth? The hydrogen on Earth is mainly tied up in water and hydrocarbons - so there is actually quite alot of it around, although it is not free. Helium is very rare on Earth, and was actually first discovered in the atmosphere of the Sun. (In fact, that is why they called it "helium" - because Helios is the Greek word for Sun.) We don't find these elements as free gases on earth because they are so light, but we find them more in the giant outer gas-ice planets.
Back to the early solar nebula: In the center of this swirling gas cloud, or nebula, the density and temperature got high enough for a star to form and begin thermonuclear reactions in its core and shine. (That was the Sun.) In the early years of the Sun's life, it blew off vast amounts of gas and charged particles - solar wind. We believe that the planets formed as the solar nebula cooled down, and the planets "froze" out of the hot gases. Iron and Nickel have the highest melting/freezing temperatures, so they could condense out closest to the Sun - that is why Mercury, the closest planet is mostly made of iron and nickel compounds. At the distance of Earth, it was cool enough for iron, nickel, and rocks to condense out, but because iron is much heavier than silicon dioxide (quartz), the iron and nickel sank to the center of the earth forming the core, while the rocky material crystalized to form the crust of the Earth. Farther out, where Jupiter, Saturn, Neptune, and Uranus are found, it was cool enough for gases to crystalize into ices, and so those planets are made mostly of the ices of water, methane, ammonia, and hydrogen. Jupiter has a strong magnetic field, but little or no iron in it, so its core might be made of liquid hydrogen, which behaves like a metal but is very light.
So - to summarize, your question has two parts: the abundance of iron and silicon is greater than the heavier elements in the universe in general, and the earth is at the right distance from the Sun so that when it condensed out of the solar nebula, the ligher elements were either bound up in compounds or blown away to the farther reaches of the solar system.
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