Terraria's objectives are to craft and to build. Both of these are handled by gathering resources from different biomes within the game. Each of these resources provides different advantages to both building and fighting enemies.
The player's first objective is to chop down trees using the starter axe, according to Gamepedia.com. The player should build a workstation to upgrade his weapons to fight enemies.
The player should also be exploring the world of Terraria and gathering resources to build better weapons and better forts to fight enemies. When a boss level monster is killed, NPCs like wizards and merchants come to the player's fort to provide services to the player not otherwise found.