Exploration Goals are present on every open world map in the game. On maps with exploration goals, they will be shown on the right side of the screen under the Minimap. Completing these goals awards players exploration stars (one for each goal), Experience, and Mesos. Players can check their exploration progress in the World Map at the top left. The Show/Hide button toggles a view of exploration stars achieved for all of the maps. Under that button is a showcase of rewards that players can claim when they reach certain star thresholds.
Some exploration goals can be vague or detailed. For a guide about how to complete the specific goals, you can look at this guide: A Guide to the Stars (Exploration Guide).