The fundamental interactions or fundamental forces are the most elementary forces of the Universe, in the sense that they are not reducible to more elementary components. In the modern Universe there exist four of them:
Three of these are said to be exchange interactions, which is to say that they act by exchanging discrete quanta in the form of particles known as force carriers or exchange particles. All exchange particles we know of are bosons and in the Standard Model they are collectively known as gauge bosons. These are photons for electromagnetism, gluons for strong interaction and W and Z bosons for weak interaction. As such, these interactions are understood as a part of quantum mechanics.
The remaining interaction, gravity, is only understood outside of quantum physics. The modern theory of gravity is Einstein's theory of general relativity, in which it is the curvature of spacetime that enacts the force. The explanation of gravity as a quantum phenomenon and the potential discovery of the quantum of gravity (the so-called graviton) is one of the largest unsolved mysteries of modern physics.
Comparison between fundamental interactions requires a common ground, namely a set of dimensionless constants that represent the "strength" of the force with respect to the others, called coupling constants. The definition of this constant changes for each force and is partially a matter of convention as they all rely on a reference quantity. Either way, the physically significant values are the ratios of the constants, which are independent of convention provided the same convention is applied to all of them. These are
This is the general hierarchy of interactions. Strong is aptly named for being the strongest, followed by electromagnetism, weak and finally gravity. You'll notice massive differences in orders of magnitude, especially between gravity and the others. The reason why such a colossal jump in strength exists between gravity and weak force is currently not understood and is known as the hierarchy problem.