If one descends to smaller and smaller scales one always finds that larger things are built up from smaller things. When one looks to a human, she is made from cells. Each cell in turn is built from molecules, small and large.
Each of the molecules, in turn, is made from atoms. These atoms are rather small, like 0,0000000001 m each. There is one thing special about atoms which has not been encountered with molecules and cells: There is only a finite number of different ones of them observed in nature, while there appears to be an infinite number of different molecules and cells. In fact, atoms can be organized into a scheme (ok, this also applies to molecules and to some extent to cells also), the so-called periodic system of atoms. There are roughly hundred of them to be found in nature, and we managed to make a number artificially of them more over the years. Each of the atoms differs by its chemical properties.
So, it seems that atoms can be built, much like molecules. However, it is found that there are some atoms which behave in every respect essentially identical when it comes to chemistry, but they have a different mass. Both facts (and a number of others) suggest that atoms themselves are built from other things.
Indeed, it is found that atoms are made from two parts: Electrons and nuclei. The electrons orbit the nuclei, which is about 100000-times smaller than the atom (the electrons are even smaller as discussed previously). The are different electromagnetically charge with respect to each other, and there is always exactly one nuclei, but so many electrons that the total electric charge is zero.
It turns out that the charge is responsible for the chemistry, so the charge of the nuclei characterizes the atom. The mass of the atom is made essentially by the nuclei, which is about 2000 times heavier than the electrons. So different mass nuclei provide the same chemistry. Why?
Well, it turns out that the nuclei are composed from different objects themselves, the nucleons. That is the reason why new ones can be made and there are chemical identical ones with different mass. They nucleons come in two types, the neutrons and the protons. The latter carry the charge, making the atom chemical active, while the neutrons are chemically essentially inactive. On the other hand both have essentially the same mass. So chemically different atoms differ by their number of protons, but chemically identical atoms having different mass differ by the number of neutrons.
It is found that the nucleons have about the same size as the nuclei, so they are fairly densely packed inside the nuclei (in a typical atom there are a few dozen nucleons). What is keeping them together? It cannot be gravity alone, as it is too weak. If gravity alone should provide this, the nuclei would be much, much larger. It cannot be electromagnetism, as the neutron has no charge. So it must be something different. Indeed it is a new force, the so-called strong (or, since it was discovered in the context of the nuclei, nuclear) force. This force is binding the nucleons together to form the nuclei, and thus shapes the very word we live in as much as electromagnetism does.
The force between the nucleons is created by the exchange of mesons. These particles are usually not observable in nature as they decay too fast by the weak interactions to be discussed later. They can be observed in cosmic rays. The most important meson is the pion, having about an eighth of the mass of the nucleon. So, in contrast to the photon, it is massive. It also can carry charge, there is a positive one, a negative one, and a neutral one. There are also other mesons, the kaon, the rho, and the omega, playing a role in the nuclear force. In fact, as it was started to investigate this, more and more of these mesons have been found. Also, it was found that the nucleons are not the only of their kind. There are other, quite similar objects, like the delta or the cascade particles. Those nucleon-like particles have been termed the baryons, in distinction to the mesons. Both together are called hadrons, to distinguish them from the leptons. These mesons and baryons can again be put into a kind of periodic table, and we can produce new ones of them.
As the experience with atoms already told, this indicates that the baryons and mesons are themselves composites from other particles. Indeed, they are built up from quarks. Mesons consists of two, baryons of three quarks. If there are objects which are constructed from four or five or more quarks is not really known. If so, they are rathe short-lived and decay into mesons and baryons. During the recent years, conflicting experimental results made this a hot debate, and the judge is still out. These objects would be called tetraquarks (four quarks) or pentaquarks (five quarks).
In any case, there has to be a force holding the quarks together inside mesons and baryons. It turns out that this is again the strong force, but in another disguise.