Photons are energy packets that carry the electromagnetic force: whenever two particles interact via this force, they exchange a photon. Photons allow atoms to exist: the negatively charged electrons on the atomic shells are bound to the positively charged nucleus via a continuous exchange of photons.
Photons are massless and therefore travel at the maximum velocity, the speed of light. The speed of light in vacuum is a fundamental constant set at 299’792’458 m/s, which is used, for example, to define the unit of metre.
We experience photons as electromagnetic waves in many different ways: as visible light, heat (infrared radiation) or to get tanned (UV light), we use them to see our bones (X-ray scans), talk on mobile phones or heat our food (Microwaves).
Photons can also have particle properties as quanta of energy. This idea was initially proposed by M. Planck in 1900, and extended by the photoelectric effect conceived by A. Einstein in Bern in 1905: photons as particles can transfer momentum to electrons and eject them from a surface exposed to light which would not be possible by a wave, which would only shake the electrons.