When it comes all the way down, it’s clear that we don’t know the definition of an electric field. We do are able to create them, identify them and then use them to accomplish amazing things.
Electromagnetics can be described using Maxwell’s equations. One of the equations states that a changing electric field E creates the formation of a magnetic field that changes in time. Another equation states that a magnetic field that changes in time H will cause a time-changing electrical field. Both equations predict waves due to the fact that an E can induce an H that will trigger another E, which in turn will cause another H and it goes on. The electromagnetic waves (radio waves such as light, x-rays and so on.) each has the electric field as well as magnetic field. It is the interaction between them that causes waves.
In DC we can experience electric fields that are not magnetic. Rub your feet over the carpet, or touch metal objects, and be shocked. It’s an electromagnetic field (many thousands of Volts) which breaks down the air, causing an electric arc.
Electric fields can force things. Have you ever noticed someone’s hair standing up when it’s dry? Electric fields push the hair. If you apply pressure to a balloon your head, you could put the balloon in the side in a manner. Electric fields trigger this attraction.
Electric fields can also drive charges. In many cases, this is the cause of electrical current. Batteries create an electric field which moves electrons along a wire. Magnetic fields also create current, such as in the alternator in your vehicle.