Just as with a gravitational system, two two charged particles, zero potential energy represents the state of the particles when they are infinitely far apart. With opposite charges, all other values are negative. The two charges fall together into a well of their mutual binding energy. How far below zero represents the work that would be required to completely separate the particles.
As we discuss the fundamental principles of Work, Power & Energy, keep in mind that electrostatic systems will be a primary field of application for these concepts. When a positive charge is moved towards another positive charge, potential energy increases. Energy is being stored in the system. However, when a negative charge is moved towards a positive charge, potential energy decreases and the system is losing potential energy.
The behavior of oppositely charged particles, distinguished by a force of mutual attraction, is similar to gravitational force. The energy description of oppositely charged particles is analogous to the behavior of two masses interacting through gravitational force. The nearer the objects, the lower the potential energy with both gravitational force between masses and the electric force between unlike charges.