Potential energy is energy that can be released, e.g., to push on something, basically energy that is not kinetic energy. Everyday examples include the energy in a spring under tension, or the energy in a weight some distance above the Earth, both of which have been used in mechanical clocks to provide the energy to make them run. Chemical and nuclear energy are also potential energy (or, at minimum, includes some).
There is potential energy in any two objects sharing a mutual force, e.g., gravity, so the Earth's position relative to the Sun has a certain amount, or an atom's electron's position relative to the nucleus. For items attracting each other, a common convention is to list the potential energy as negative, the amount of energy required to pull them completely apart. In the case of gravity, this equals the kinetic energy the item would need to travel at escape velocity. In the case of an atom's electric force, this equals the energy necessary to ionize the atom, i.e., draw the electron completely away from the nucleus. (In both cases, the force is there at any distance, the velocity/energy is just enough to put the one item on a course where it would never slow enough to return, if there were no other influences.) The "negative energy convention" makes the math of summing kinetic and potential energy both before and after some activity show the conservation of energy: so the resulting sums are equal.