June 02, 2021
First, it's been thought that electromagnetic forces were applied instantaneously between charged particles. But later experiments showed that it's not the case, there is an infinitesimal delay. If you make one particle oscillate around a position, another particle close by will feel the electric force, with a varying intensity (corresponding to its physical displacement) but with a small phase shift. This has big implications in terms of physics.
Let's take the parallel of two floating tennis balls in a pool of water. If the two tennis balls are close enough, you could quickly move the first tennis ball and this will induce the second to move; through the water. If you didn't see the water, it would be like applying a force onto the second ball using the first one; just like the electric force. If the two balls are too far apart, you cannot do the same, i.e. the force that you can apply on the second ball depends on the distance. Now, if you make the tennis ball oscillate in the water, this will make the second ball move in a different way; because you created waves into the water. These waves propagate on the water surface and can have an effect much further away.
This phase shift in the propagation of electric/magnetic forces means that it is possible, much like in the water analogy, to create electromagnetic waves. But waves usually propagate through a medium, and so physicists invented a name for this medium: a field. The electromagnetic field was born. The electromagnetic waves can have effects much much further than the static forces would allow. They are travelling at the speed of light, which is 299 792 458 m/s.
More theoretically, a force field has actually a mathematical definition; which basically defines "a non-contact force applied to a partile at various positions in space." [Wikipedia]