Crystallization of solutions and liquids
Crystallization is rightly called by you a process.  Simplified, there are two steps to be considered: Nucleation and crystal growth.  For the sake of simplification, let me consider the crystallization of a molecular compound in absence of ionic charges.


Nucleation refers to the initial stage, where once isolated molecules of the dissolved substance assemble to a first crystal germ. This is energetically hindered because these particles of especially small size have unfavourably high ratio of particle surface energy per molecule in these just formed particle (or perhaps better: aggregates). This energetic drawback has to be overcompensated. In addition, molecules loose degrees of freedom accessible in solution, at first: dynamic freedom, and secondly, depending how strictly rules are followed to build the crystal, a number of orientations in space otherwise available and accessible--In a perfect crystal, the structural close environment of one molecule is going to be repeated for all molecules, the very next ones and for their next ones, over ranges of Angstroms to Centimetres.  


Once such a germ is formed,


Crystal growth more or less refers to simply attachment of additional molecules according to these "(energetically justified) previously determined rules" to yield a bigger entity.  The need of oversaturation of the solute is less prominent than during nucleation, yet still existent to energetically favour this process. In this description, crystal growth is again simplified, too.  It may happen, in the (sub)process of crystal growth, conditions are met that allow crystallisations in realisations even more energetically favourable than at early stages of crystal growth so that a compound preferentially forms a polymorph A initially, then ones in polymorph B. And often a crystallization does not yield only one (perhaps even single)crystal, rather than multiple ones.  So nucleation may occur in one spot of the solution while simultaneously crystal growth already takes place on germs already formed in other parts of the solution.


Complementary, think this way: it is every time easy to dissolve a perfect crystal (already considering entropy), but easily difficult to bring molecules back into a perfectly ordered crystal.

The science and art (like craftsmanship) of crystallization is of high importance in our daily life, spanning areas of electronic devices (semiconductors) till pharmaceutics. Journals like Crystal Growth &amp; Design or CrystEngComm are examples concentrating on this subject.