Photons are the quantized modes of electromagnetic field radiation.
Mathematically, this means that they are a way to describe classical light in a quantum mechanical way; a similar analysis can be made for sound, resulting in the phonon.
The photon represents a quantum state; there are definite rules that apply, which depend upon the situation. Planck's relation is very general, and relates the frequency of the classical radiation to the energy of the photon: if you know the frequency, the energy is also known: energy = Planck's constant x frequency, or E=h*f.
From an observational perspective, photons in large groups act just about how you would expect light to act: they show interference and diffraction, can deliver energy, and have momentum. They always travel at the speed of light.
But as you have fewer and fewer their unique quantum properties become more apparent: when detected, all of the energy appears at a single point, so they behave as though they are a particle. This is the origin of the photoelectric effect: light is absorbed by a metal basically one "lump" of energy at a time, based on the energy from Planck's relation. Thus if the electrons require a certain amount of energy to escape from the metal (the "work function"), there will be no electron emission for light consisting of photons with energy below that cut-off point - which results also in a frequency cut-off. This is why the photoelectric effect is independent of the intensity of the light.
There is a lot more that can be said; I refer you to Richard Feynman's book & lecture, "QED: strange theory of light and matter". The four-part lecture series can be found on the web.