What is a field?

[KipIngram]

Kjelleman: When you listen to the FM radio in your car, your radio is receiving signal energy initially produced in the station's transmitter. That energy got from the transmitter to the receiver via the field. So fields can possess and transfer energy; that makes them seem pretty real to me and not just a calculation technique. From what I've read they can possess and transfer momentum as well.

 

My own working definition of a field in physics is the association of a value with all points throughout a region of space / spacetime. That value can be scalar, vector, tensor, whatever.

[Mordred]

Excellent definition it pretty much sums up a field