Your main objective is to survive It's sometimes really difficult because lava is in angry mood and eats things that stands on its way. Even solid blocks are sometimes melted so it's wise to keep walls thick and you should hope that no earthquake occures (in development stage).
At the end of the round there's list of winners and their score. If you want to get high score build big. The more space (air) around you the higher the score. And being above the sea level at the end also boosts your score (check with /position). Easy way to get higher score is to find a pal that you can build with. Your best score is stored and you can check it by typing /score in-game.
Also score adds up to your experience. You can check your experience by /score or /look command. /look you can also use on other players. Your current level is showed in () next to your name. When you reach certain experience amount you level up. The second level requires 500 exp.
But the most important thing is just to have fun of playing and feeling like the adventurer that shelters himself/herself from the coming doom ^^