As you progress through the storyline in Urban Legions, you will encounter various objectives. Major objectives and plot points will be recorded in your list of quests. Depending on your progress with a quest, it will be labeled as either "Active" (meaning, there is still something more to do before the quest is complete), or "Finished" (meaning, you have completed the task set before you for a given quest).
Since the developers of Urban Legions are constantly adding more content to the game, some quests may stay active for quite a while. The means of completing some tasks may not be solvable until a later time in the game's storyline. Check back periodically and see if you a quest is able to be completed, but do not get too frustrated when you are at a temporary empasse.