Here's a general outline of what often happens:
* The Legendaries' Role Changes: The freed legendaries might become more active, their powers strengthening, or they might choose to protect a specific location.
* The Story Continues: After freeing the legendaries, you often face a new threat or a new challenge related to them. This might involve defeating a villain who wanted to control them, or it might be a natural event that needs your help.
* New Areas Open Up: The legendaries might open new areas for you to explore, or they might unlock new abilities for your Pokemon.
* Post-Game Content: Many Pokemon games have post-game content that involves catching the legendaries, training them, or using them in battles against other trainers.
Examples:
* In Pokemon Ruby, Sapphire, and Emerald: After freeing Groudon and Kyogre, you face the threat of Rayquaza, a legendary Pokemon that tries to balance their powers.
* In Pokemon Diamond, Pearl, and Platinum: After freeing Dialga and Palkia, you face Giratina, a legendary Pokemon from a different dimension.
* In Pokemon Black and White: You encounter the legendary Pokemon Reshiram and Zekrom at the end of the game, and the story revolves around their power and the conflict between them.
To give you a more specific answer, please tell me which Pokemon game you're interested in! I can then tell you the specific events that happen after you free the legendary Pokemon in that game.