Electromagnetic force is the interaction between electrically charged particles like protons and electrons. It is one of four fundamental forces in the Universe, other three being gravitation, the weak interaction and the strong interaction. Particles with electric charges create electromagnetic fields which in turn affect the behaviour of electrically charged particles and objects in its vicinity.
Electromagnetic force is what keeps negatively charged electrons bound to positively charged protons in atomic nuclei, thus creating atoms with no electric charge.
Except gravitation, the electromagnetic force is the one responsible for most of the phenomena we encounter in our daily life. All other, non-fundamental forces can be explained by the electromagnetic force acting on protons and electrons inside the atoms and how these two particles carry momentum between atoms and molecules. All chemical reactions involve electrons affected by the electromagnetic force.
Although electrons play essential part in all chemical reactions and non-fundamental forces, photons are actually carrier bosons for the electromagnetic force. They are massless and carry the electromagnetic force over unlimited distances. Photon is a quantum of light, where light is just a visible part of the electromagnetic radiation. We explore the Universe mostly by observing sources of electromagnetic radiation, including light, with our telescopes. More on that later.
Both magnetism and electricity were known since ancient times, but it wasn’t until 1820 that it was realised they were part of the same phenomenon. Electricity is the flow of electric charge between atoms, carried by electrons but caused by the electromagnetic force. Spinning, electrically charged electrons are what causes magnetism on a larger scale, but in its essence, it is the same force that causes electricity.
When a photon, which doesn’t have electric charge, hits an electron in an atom, it “excites” the electron i.e. transfers its energy to the electron. When that electron stabilises, it releases extra energy by emitting a photon. This is what happens in many instances, but as an example, let’s take a microwave oven. Electromagnetic radiation is carried by photons at microwave frequencies (3 GHz - 300 GHz). These photons excite electrons in your food’s molecules, making the food warm and generally more fluid because bonds between molecules are weaker.
Speaking of microwaves, they are part of the electromagnetic spectrum. Electromagnetic radiation is a radiant energy released by electromagnetic processes. It can be divided, from highest energies i.e. frequencies, into Gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves and radio waves. It is, of course, carried by photons. Because of wave-like properties of photons, these energies have their wavelength and frequencies. Simply put, light and colours you see are nothing more than photons transferring their energy to electrons in your eyes.