The boys explore the island multiple times throughout Lord of the Flies, but some of the most significant discoveries happen on the first day after the plane crash.
Piggy and Ralph explore the scar and discover the trail of destruction left on the island. Piggy guesses that the fusilage of the plane was dragged out to sea. Piggy and Ralph also discover the conch and use it to call the other boys to the first meeting.
Ralph, Simon, and Jack explore the island as 'scouts' for the other boys. They discover that the island is uninhabited, has fresh water, fruit, and even meat in the form of pigs. They also are the first to climb the mountain. Later, Ralph reports back to the boys, proud of their discoveries and informs the others that "this is a good island."
If by boys you are reffering to Ralph and Piggy, they discover a conch shell which serves as a symbol of civilization throughout the story (when the conch is shattered, so are any remains of civilization.)