A photon is a particle of light
(or of any electromagnetic radiation), i.e., a term for
such a particle, when light is considered a stream of particles.
The particle represents the quantum of light, the minimum possible amount.
The photon theory, i.e., the modern particle theory of light,
posits the minimum possible amount of light depends upon the light's wave
frequency.
Dating from prior to photon theory, there has been a very successful
opposing theory that EMR consists of waves, which is consistent
with experimental evidence and with a wave-structure inherent in
Maxwell's equations.
Photon theory coexists because it is successful in modeling
some light/matter interactions that the wave theory does not.
According to current particle physics, photons are elementary
particles (a type of boson) that interact with other particles.
They naturally travel "the speed of light", which in a vacuum
is the well-known constant, and even when not in a vacuum, they
are merely slowed yet still moving.
As implied above, a photon has an associated "light-wave frequency"
and carries an amount of energy proportional to that frequency
(photon energy, typically measured in electron volts).
They have no mass (i.e., no rest mass), which semantically
follows from the fact that they "cannot be at rest", but some effects
of rest mass can be tested (detecting velocity dispersion in a
vacuum or its equivalent) and are indeed checked when opportunities
present themselves (astronomical phenomena producing measurable
dispersion), basically providing evidence in support of
the theory of relativity
Phenomena apparently requiring photon-theory to explain include the
interactions of light with atoms and electrons, such as absorption,
emission and scattering. The first such instance
explained by photon theory was the photoelectric effect, i.e.,
that the ejection of electrons which can occur when EMR
strikes a metal surface ("metal" as in copper, silver, etc.)
does not depend upon the total light energy striking the surface,
which only happens with a sufficient EMR frequency,
can be explained if light arrives in quanta based upon
frequency, and only frequencies associated with sufficient energy
to free such an electron succeed in doing so.
Einstein pointed this out in one of his 1905 papers.