An electric field describes the region of space around an electrical charge (or between two charged plates) where a second charge would feel an electrical force.
Around a single charge (like a hydrogen nucleus), the strength of the field decreases with distance. The force between the two charges (the source of the field, and the charge in the field) can be calculated using Coulomb's Law. Without going into the math, the force is proportional to the product of the two charges and inversely proportional to the square of the distance between them.
If the charge placed in the field is free to move, it will accelerate due to this electrical force. If the charges are opposite, they will attract. If the charges are alike, they will repel.
Electrostatic forces are called field forces because they act at a distance (like gravity). In chemistry these forces are the basis for bonding (attractions between oppositely charged ions, mutual attraction between nuclei and a shared pair of electrons) and other things like VSEPR theory which determine molecule shape.