The electric field of a charge density at a specific point in space tells you the direction and magnitude of a hypothetical force, ie. how many Newtons of force would be exerted per Coulomb of hypothetical test charge if we were to introduce it at the point.
When you speak of the electrical or gravitational field of an object, you are describing the capability of that object to exert force. Think of it as a capability permeating the space around the the mass or charge producing the gravitational or electric field respectively.
The stronger the field at a given position in space near the object, the stronger the interaction which would occur if another mass (gravity) or charge (electricity) were introduced at that position relative to the field producing object. For a single spherical mass (gravity) or point charge (electricity), field lines can be drawn spreading out in space (diverging) to show that the field is decreasing in intensity with increasing distance from the object.
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