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Are you asking for a definition? They represent how strongly an object placed at a particular point will be affected by electric, magnetic, or gravitational forces. Say you place an uncharged particle of mass m at some point and measure the force on it (F). The (Newtonian) gravitational field is then defined as g=F/m. You make a similar construction for electric and magnetic forces.
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You've explained very well what they do, and how they act, but not what they are.