A spontaneous process is a process which is capable of proceeding in a given direction after proper initiation under a given set of conditions.
All natural processes are spontaneous processes.
A spontaneous process moves in that direction in which (a) energy is minimum and (b) entropy or randomness is maximum.
Flow of heat from a hot object to cold object is an example of a spontaneous process.
Boiling of egg is also a spontaneous process. This seems strange but it can be explained by randomness. When an egg is boiled, the hydrogen bonds of protein molecules break and the randomness increases. Due to increase in randomness, this process is spontaneous.
Other examples of spontaneous process are: rusting of iron, salt dissolving in water, diffusion of a gas in container etc.
The laws of thermodynamics govern the direction of a spontaneous process, ensuring that if a sufficiently large number of individual interactions (like atoms colliding) are involved, then the direction will always be in the direction of increased entropy and decreased Gibbs Free Energy.
Change in Gibbs Free energy (ΔG) is negative in case of spontaneous process.
Change in entropy (ΔS) is positive in spontaneous process.
The process which cannot occur on its own even after proper initiation under a given set of conditions is known as non-spontaneous process.
For a non-spontaneous process, entropy change will always be negative (ΔS < 0), ie, entropy will decrease making the system unstable.
Change in Gibbs Free Energy (ΔG) will also be negative for non-spontaneous process.
Upward flow of stream of water is an example of non-spontaneous process.
Endothermic reaction at very low temperature is also an example of non-spontaneous process. Similarly, exothermic reaction at very high temperature is also an example of non-spontaneous process.