The Questlog contains all the information about the quests that you've accepted and solved in the world of Antaloor. This source of information is closely associated with the map function - and that's why they're adjacent to one another on the right hand side of the map interface. To help you keep track of everything, the Log is divided into two sections - the Main Quest, 'Tainted Blood' and the secondary quests.
Quests are what players will spend most of their time doing in Two Worlds. They are one of the best, and quickest ways, to gain Experience Points, Gold and Reputation. See the Quest Guide page to see a list of Quests.