GENERAL DEFINITION Happiness is the factor in your city which determines whether or not people will be able to / want to, move into your city. This dynamic effectively limits your population and forces you to use your factories wisely in order acquire more money to build more advanced leisure buildings to raise your happiness level.
HOW IT WORKS
In general, when your "happiness score" (i.e. the sum of the numbers displayed alongside the leisure buildings and some terrain features) is higher than your population, the face at the top is a purple happy face. While the face is happy people are free to move into your city without any problems and you can swiftly increase your population.
When your "happiness score" is equal to or just above your population the face turns to a neutral yellow face. This face indicates that you are nearing the threshold to where no one will want to move into your city.
****note**** I do not know at what point the face goes to the blue sad face, I'll let my city expand until it happens and update the last part. In general though if your face is the sad face your people will not want to move into your city. When this happens you cannot increase your population or advance in city type until more leisure buildings are built. You can still run the factory (very recommended) and collect XP.
WHERE DOES HAPPINESS COME FROM
Happiness comes from anything from the leisure building section, and the terrain section. The higher scoring leisure buildings are generally the ones that require "City Bucks" although there are coin purchasable options that will advance happiness quite a bit.
Try not to go overboard with residential buildings and forget comletely about leisure buildings or terrain features. Sometimes terrain features can be the ones that can save you from unhappy people.
Take advantage of neighbors and gifts from people to advance the happiness.
****more to come****