An object is in a stable position if it has no tendency to move. It rests inside a potential well, which is a minimum at the position of the particle as shown below..
If the particle is at a maximum for the potential it is in an unstable position. It will tend to move towards a position of minimum potential energy. This is a fundamental concept. Particles always tend to move so as to minimise their potential energy.
Objects fall to the Earth so as to minimise their gravitational potential energy.
An object on a stretched spring will move so that the spring contracts, minimising the elastic potential energy of the spring.
Particles of the same sign electric charge will move away from each other so as to minimize the electric potential energy of them both.
Liquids usually have a flat, not curved surface so as to minimize the sum of the graviational and surface energies. It may be curved at the edges, for example, where water touches glass. This is because surface tension dominates over gravity, but it is still the sum of surface potential energy and gravitational potential energy that is minimized.