spontaneous process
Let go of a ball at the top of a hill and it rolls down by itself; you never see it climb back up on its own. Open a perfume bottle and the scent drifts across the room; it never crowds itself back into the bottle. A spontaneous process is any change that, once nudged or allowed to start, proceeds on its own without a continuous outside push.
In thermodynamics, 'spontaneous' has a precise, unromantic meaning: a process is spontaneous in the given direction if it increases the total entropy of the system plus its surroundings. For a process at constant temperature and pressure, the handy shortcut is that the Gibbs free energy must go down. It says nothing about speed — only about direction.
Why it matters: spontaneity tells you which way a reaction or change is allowed to go without help, the foundation for predicting equilibrium and designing reactions. The crucial caveat: spontaneous does not mean fast. Diamond turning into graphite is spontaneous, yet it takes longer than the age of the universe. And 'spontaneous' does not mean 'no trigger needed' — a log is spontaneously flammable in air, but you still have to light the match.
Iron rusting in damp air is spontaneous: the products sit lower in free energy than the iron and oxygen they came from, so the change is downhill. A scaffolding of catalysts can speed it up or slow it down, but nothing has to keep pushing for it to happen.
Spontaneous = allowed and downhill in free energy, not necessarily quick.
A reaction can be spontaneous in one set of conditions and not in another. Ice melting is spontaneous above 0 °C but the reverse, water freezing, becomes spontaneous below it — temperature flips the sign of the free-energy change.