Imagine you take a block of some material, say gold. You decide to split the gold and give it to as many people as you can. First you cut it in half, then you cut both halves in half, giving you four quarters. You then cut the four quarters in half, and so on and so fourth. If you continue to do this, there comes a point where you can no longer divide the piece of gold anymore. This indivisible amount of any chemical element is called an atom which comes from the word atomos meaning uncuttable in Greek.
There are three components that make up an atom. The proton, the neutron and the electron. You can combine these three particles in different ways to create different kinds of atom. The diagram below shows the structure of a typical atom. The centre is called the nucleus and this contains the protons and neutrons. The electrons are arranged around the nucleus.

Atoms are tiny. 50 million atoms in a line would measure approximately 1 cm. In addition to this, most of the atom is empty space, the nucleus makes up 99.4% of the mass of the atom. Electrons orbit the nucleus in precise distinct shells. There are limits to how many electrons can be in each shell. The first shell can hold 2 electrons, the second can hold 8 and the third 16 and so on. In the example below, an atom of carbon has 6 electrons and therefore 2 in the first shell and 4 in the second. Neils Bohr was the the first person to introduce the idea of this structure and it is today known as the Bohr model.

Each atom has an atomic number. This is the number of protons in its nucleus. Normally the number of protons and neutrons in the nucleolus is the same but the number of protons is the deciding factor as to what the element is. For example a hydrogen atom always has 1 proton. In total, there are 118 different elements, 94 of which occur naturally on Earth. The remaining 24 are synthesized in labs or during nuclear reactions.
Protons have positive electric charge, electrons have negative electric charge and neutrons have no charge. Once the number of electrons and protons are equal the atom is eclectically balanced. If the number of electrons is more or less than the number of protons, the atom is either positively or negatively charged and this is known as an ion. There are two forces which hold the atoms together. The electrons are held in place by the electromagnetic force and the protons and neutrons are held together in the nucleus by the strong nuclear force.
The theory of atoms date back to at least 440 B.C. to a Greek philosopher and scientist, Democritus. He was the first person to come up with the idea that there was a point where matter could no longer be divided into smaller pieces. His ideas were largely ignored until the 1800s. In 1897 the electron was discovered and in 1911 Ernest Rutherford discovered that atoms had a nucleus. He discovered this by firing high energy particles through a thin sheet of gold. He noticed that most of the particles got through the gold unaffected but some were deflected. In the 1900s there were a lot of developments in the area of particle physics. One of these is Quantum Theory which aims to explain the workings of nature at the sub atomic level.