The endgame begins as soon as you complete the Wall of Flesh domain and your world has entered Hardmode.
At this time you've been introduced to the core concepts of the mod such as the gearing, crafting, and mapping system.
From here you can start to participate in the end-game grind and further progress your character to take on additional bosses.
Leading up to, and including, the wall of flesh domain you may have started dropping Explorable Maps. These explorable maps can be used in the Map Device to travel to new lands to continue your adventure.
Explorable Maps will have a theme and a tier associated with them. The theme of the map will determine the type of biome the explorable map is in and the tier of the map will determine the area level and the difficulty of the map.
Completing and exploring these maps is the core foundation of the endgame system.