There are two types of goals on VDex: User Set Goals, and Daily/Weekly/Monthly Goals. User set goals are goals that you set for yourself. Completing these goals gets you no actual reward, but allows you to keep track not only of what you have done, but the goals you set for yourself to complete in the future.
Daily/Weekly/Monthly goals, however, are exactly what they sound like: Goals presented to you by the site itself. These goals award you with GP (Goal Points) when completed, which may be spent in the Shop tab.
Daily Goals usually present a small, easy challenge that can be completed within the course of a single day. Such goals include catching a few Pokemon, adopting a Pokemon, obtaining shiny leaves, and other such easy tasks.
Weekly goals are a bit harder than Daily Goals, and present challenges that can generally be completed within the span of 7 days. Such goals include planting a certain amount of berries, harvesting a certain amount of berries, capturing a certain amount of Pokemon, and other time-consuming tasks.
Monthly goals give you the length of an entire month to finish a very difficult or time-consuming task. Such goals include capturing 1 shiny Pokemon, palnting or harvesting many berries, adopting many Pokemon, and other difficult tasks.