The Standard Model (SM) of physics is a theory of the elementary particles, which are either fermions or bosons. It also explains three of the four basic forces of nature. The four fundamental forces are: gravity, electromagnetism, the weak force, and the strong force. Gravity is the one the model does not explain.

The model uses the parts of physics called quantum mechanics and special relativity, and the ideas of physical field and symmetry breaking. Some of the mathematics of the SM is group theory, and also as equations which have biggest and smallest points, called Lagrangians and Hamiltonians.

Fermions
Fermions are particles that join together to make up all "matter" we see. Examples of groups of fermions are the proton and the neutron. Fermions have properties, such as charge and mass, which can be seen in everyday life. They also have other properties, such as spin, weak charge, hypercharge, and color charge, whose effects do not usually appear in everyday life. These properties are given numbers called quantum numbers. 

Fermions are particles whose spin numbers equal an odd, positive number times one half: 1/2, 3/2, 5/2, etc. We say that fermions have "half integer spin."

An important fact about fermions is that they follow a rule called the Pauli exclusion principle. This rule says that no two fermions can be in the same "place" at the same time, because no two fermions in an atom can have the same quantum numbers at the same time. Fermions also obey a theory called Fermi-Dirac statistics. The word "fermion" honors the physicist Enrico Fermi.

There are 12 different types of fermions. Each type is called a "flavor." Their names are:

 Quarks — up, down, strange, charm, top, bottom
 Leptons — electron, muon, tau, electron neutrino, muon neutrino, tau neutrino. The electron is the best known lepton.

Quarks are grouped into three pairs. Each pair is called a "generation." The first quark in each pair has charge 2/3, and the second quark has charge -1/3. The three kinds of neutrino have a charge of 0. The electron, muon, and tau have charge -1.

Matter is made of atoms, and atoms are made of electrons, protons, and neutrons. Protons and neutrons are made of up and down quarks.  You can find one lepton by itself, but you can never find quarks alone. This is because quarks are held together by the color force.

Bosons 
Bosons are the second type of elementary particle in the standard model. All bosons have an integer spin (1, 2, 3, etc..) so many of them can be in the same place at the same time. There are two types of elementary bosons: gauge bosons and the Higgs boson. Gauge bosons are what make the fundamental forces of nature possible. (We are not yet sure if gravity works through a gauge boson.) Every force that acts on fermions happens because gauge bosons are moving between the fermions, carrying the force. Bosons follow a theory called Bose-Einstein statistics. The word "boson" honors the Indian physicist Satyendra Nath Bose.

The standard model says that there are:
 12 fermions, each with its own antiparticle;
 12 gauge bosons: 8 kinds of gluons, the photon, W+, W−, and Z;
These particles have all been seen either in nature or in the laboratory. The model also predicts that there is a Higgs boson. The model says that fermions have mass (they are not just pure energy) because Higgs bosons travel back and forth between them. The Higgs boson is believed to have been discovered on July 4th, 2012. It is the particle that gives mass to other particles.

Fundamental forces 
There are four basic known forces of nature. Three of these forces affect fermions, and are carried by bosons traveling between those fermions. The standard model explains these three forces.
 Strong force: This force holds quarks together to make hadrons such as protons and neutrons. The strong force is carried by gluons. The theory of quarks, the strong force, and gluons is called quantum chromodynamics (QCD).
 The residual strong force holds protons and neutrons together to make the nucleus of every atom. This force is carried by mesons, which are made up of two quarks. It is not fundamental.
 Weak force: This force can change the flavor of a fermion and causes beta decay. The weak force is carried by three gauge bosons: W+, W-, and the Z boson.
 Electromagnetic force: This force explains electricity, magnetism, and other electromagnetic waves including light. This force is carried by the photon. The combined theory of the electron, photon, and electromagnetism is called quantum electrodynamics (QED).
The other force affects all particles (fermions and bosons) and is not known to have an associated boson.
Gravity: This is the only fundamental force that is not explained by the standard model. It may be carried by a particle called the graviton. Physicists are looking for the graviton, but they have not found it yet.

The strong and weak forces are only seen inside the nucleus of an atom. They only work over very tiny distances: distances that are about as far as a proton is wide. The electromagnetic force and gravity work over any distance, but the strength of these forces goes down as the affected objects get farther apart. The force goes down with the square of the distance between the affected objects: for example, if two objects become twice as far away from each other, the force of gravity between them goes down to a quarter (22=4).

Limitations 
The standard model falls short of being a theory of everything. 

 It does not include the full theory of gravitation as described by general relativity.
 it does not explain the accelerating expansion of the universe (as possibly described by dark energy). 
 The model does not contain any dark matter particle that has all the properties observed in observational cosmology. 

The standard model is believed to be theoretically self-consistent. It has demonstrated huge and continued successes in experimental predictions, but it does leave some things unexplained.

References

Other websites 
 A school site: Explaining the Standard Model
 Standard model Citizendium

Basic physics ideas
Relativity
Matter
Nuclear physics