In simple terms a Field is an 'area of influence' around a body. A charge, for example sets up a field around it - an area where the charge can be 'felt' (by bodies that feel the Electromagnetic force).
Potentials are related to Energy. In a field, different positions would give an object placed there, different amounts of energy. For exampmle a body on the Earth's surface will have a different amount of GPE than a body a million miles away from the Earth. The unit of Potential helps explain the concept - J/kg for a gravitational potential, and J/C for Electrical potential.
You can think of the Gravitational Potential of a point as being the work that would be done in moving unit mass from infinity to that point. Similarly with electric potential - this is the work that would be done in moving unit charge from infinity to that point.