Fundamental interactions are interactions that cannot be reduced to more basic interactions. There are four known to exist:
Gravity
Electromagnetism
Strong nuclear force
Weak nuclear force
Gravitation and electromagnetism produce significant long range forces that can be observed in everyday life through their effects. The strong and weak nuclear force act over a much shorter range, subatomic distances, governing nuclear interactions. The hypothesis that there may be a fifth force, remains only speculative.
Each of these forces can be mathematically described as a field. The gravitational force is related to the curvature of spacetime. This is described by Einstein's general theory of relativity. The other three are distinct quantum fields. Their interactions are mediated by subatomic particles. These particles are described by the Standard Model of particle physics.
In the Standard Model, the strong nuclear force is mediated by gluons. Gluons are responsible for the binding of quarks into hadrons. For example:
Protons - are 3 quarks (a baryon), 2 up quarks and 1 down quark
Neutron - are 3 quarks (a baryon) 2 down quarks and 1 up quark
Gluons bind quarks into atomic nuclei.
The weak nuclear force is carried by the W and Z bosons. These particles mediate radioactive decay.
The electromagnetic force is mediated by the photon. Photons create electric and magnetic fields. Photons constitute visible light. The electromagnetic force is much stronger than gravity. It tends to cancel itself out within large objects. Thus, over large distances, gravity tends to be the dominant force. This is the scale of planets and galaxies.
Many physicists believe that these fundamental forces are related to each other, are unified and become one force at very high energies on a minuscule scale. This is the Planck scale of 10^-35 meters. Particle accelerators cannot produce the massive energies required to experimentally probe this. Devising a common theoretical framework that describes the four fundamental forces is a major goal of today's theoretical physics.
The electromagnetic and weak nuclear forces have already been unified in the electroweak theory of Sheldon Glashow, Abdus Salam, and Steven Weinberg. These theorists received the 1979 Nobel Prize for their work. Progress in uniting the strong with the electroweak fields exists within the Grand Unified Theories. The biggest challenge, however, is quantizing the gravitational field. This would result in a theory of quantum gravity. This would unite gravity with the other three fundamental forces. There are theories, like string theory, that utilize quantum gravity, unify one framework, in a theory of everything.