Views, Unique Views, and Clicks are statistics that determine if your egg will hatch and if your hatchling will grow. Views are accumulated every time someone views the actual image of your egg/hatchling/adult. Unique Views are obtained in the same way, except only one unique view is given per egg per person. A "click" occurs when someone clicks on your egg in your signature or wherever you place it, and views the page that contains all of the information about your creature. As with Unique Views, clicks are only given once per person.
Your clicks, views, unique views, and the amount of time that has passed since the dragon last changed stages are variables in a mathematical function that produces a fictional 'score' for your dragon. An egg's 'score' must reach a certain amount before it will hatch, and a hatchling's 'score' must reach an even higher amount before it will mature.