Types of Equilibrium
Stable, unstable and neutral equilibria
A cone sitting on its base is in a state of stable equilibrium. The downward force of the cone's weight, acting through the centre of gravity is balanced by the reaction force of the ground. The reaction force is equal in size, opposite in direction and perfectly aligned to the weight force. If the cone is pushed aside, the cone's weight still acts through its centre of gravity, but the reaction force is no longer aligned. The reaction now acts at the point of contact between the cone's edge and the ground. The two opposing and misaligned forces create a couple which produces torque tending to twist the cone towards the original, equilibrium position - and can be perceived as the cone "pushing back". Irrespective of which direction the cone is pushed, the reaction force acts to return the cone to the original, equilibrium state, which is why it is termed "stable"
A cone balanced on its point is in a state of unstable equilibrium. As before, the downward force of the cone's weight, acting through the centre of gravity is balanced by the reaction force of the ground. If the cone is pushed aside - even infinitesimally - the couple created by the two opposing and misaligned weight and reaction forces produce torque twisting the cone even further from the initial position and the cone will swiftly topple. An unstable equilibrium is more than anything a theoretical curiosity - at best it could only exist as a transient state
Neutral equilibrium is a special case where no state is more favourable than another e.g. where the cone is lying on it side
Static and Dynamic Equilibria
The former three examples - stable, unstable and neutral - are all static equilibria. In chemistry, in biology and in some physical systems a state of dynamic equilibrium can exist. So consider a reversible chemical reaction where two reagents, A and B react to form a product C:
A + B ⇄ C
At first, only A and B are present. Later some C is formed, the reaction is proceeding. Given sufficient time the reaction will reach equilibrium - with A, B and C all reaching a constant, equilibrium concentration. At a macroscopic level, the reaction has - apparently - stopped, nothing is "happening". At the molecular level, however, A + B are continuing to form C - and C is continuing to decompose into A and B at exactly the same rate. This is dynamic equilibrium.