New Game Plus (also written New Game +) is a recurring feature of the Chrono series: when the game is completed you may play through again keeping everything you had from the first playthrough.
With the New Game + feature, one is able to keep all of their items, their status, etc. It also allows the player to even access certain endings that are not able to be received the first playthrough.
In Chrono Trigger, the New Game + feature is the only way to get the special Developer's Room ending. To achieve that ending, Lavos needed to be defeated before testing Lucca's Telepod and traveling to the Middle Ages. By doing so, Lavos is fought with only Crono and Marle. While most endings are achievable without a New Game Plus game save, it is easier to view all endings this way. Another ending exclusive to New Game+ is The Frog Ending. To get this ending, fight Lavos through the right Telepod after rescuing Queen Leene from Manolia Cathedral.
In Chrono Cross, the New Game + feature allows far more than just a single ending. It grants many different new items such as starting off with the Relief Charm and the Time Egg granting access to fighting the Time Devourer at any point in the game which will grant the ability to view the other endings by defeating the Time Devourer at different points in the game. Also with a New Game+ by holding L2 you can slow down the game or speed it up with R2. New bosses become available in the Bend of Time: Ozzie, Flea, and Slash. You lose your Key Items, including the Chrono Cross and the Mastermune. Lastly, it is possible to use the Chrono Cross once you get it back to get all of your characters from your previous game file including Harle but excluding Lynx.