Challenges are a kind of Achievement system in Black Desert Online which you will only see if you hit 'Y' (default) or click the little rolled parchment symbol on the right bottom of your screen.
Once the challenges are met you receive rewards which are usually items but some give you Titles. You need to claim the reward items from the Challenge/Task page manually.
Some Challenges are for doing certain things ingame a certain number of time, finding certain items or achieving a certain skill level. Others are timed for playing a certain amount of time or such. And a few are available only during events and then will be claimable for example every day you log in during the event (examples are the Valencia seal in celebration of the addition of Valencia). As there are daily rewards/challenges you should open the Challenge/Task tab every day you log in.