The Post-War Arc includes the following characters: Monkey D. Luffy and various Straw Hat Pirates, Jinbe, Boa Hancock, Trafalgar Law, Silvers Rayleigh, and Marine officials like Garp, Smoker, Tashigi, Koby, and the Admirals Sengoku, Akainu, Kizaru, and Aokiji.
The first purpose of this arc is obviously to sort out the consequences of the Marineford War and Ace's death by focusing on Luffy's recovery and the repercussions of the war on a global scale. The locations used in this arc range from Amazon Lily, through Marineford, to finally the island where Luffy will start his training.
The Plot of the Post-War Arc commences instantly after the Marineford War, where Luffy, Jinbe, and the Heart Pirates go back to Amazon Lily. Luffy is in such deep emotional distress after Ace's death. The storyline centers on Luffy digesting this loss and acceptance of his weakness. Here, the world is portrayed as a place reacting to the outcome of the war, whereby tremendous shifts in power balances between the pirates and the World Government occur.
A very pivotal moment in this arc is when Luffy, still filled with sorrow, revisited Marineford with Jinbe and Rayleigh. The visit did a few things: it put up respect for the deceased, passed on a discreet message to his crew, and began the process of moving on. Deciphered, the message told them to train independently for two years, then meet again.
The arc also explains in detail what happened to other characters and their reactions to the events that happened after the war. This includes the Marines reorganizing their forces, pirates jostling for new positions of power, and the Whitebeard Pirates going through the loss of their captain. All of these events around the world work to further emphasize the lasting effect the Marineford War has had on the series and set up future conflict.
A large chunk of the arc consists of flashbacks of Luffy's childhood, mostly of his relations with his brothers Ace and Sabo. These explain much more about Luffy himself, his relationship with Ace, and the roots of his dream to become the Pirate King. Though some viewers might do so, it wouldn't be a good idea to skip through these flashbacks, as they are important in comprehending Luffy's motivations and the depth of what he has lost.
The arc reaches a climax where Luffy, with the guidance of Rayleigh, decides to have a strong and intense training session so he can become stronger. It was Luffy's first step toward conquering his grief and being prepared for the hardships in the New World. Rayleigh took him to a remote island that changed seasons at fast rates, thus offering a variety of situations and challenges in which he could test his training.
The Straw Hat Pirates finally reach the end of the Post-War Arc, where they start their personal training regimens around the world. Luffy begins his two-year training regime with Rayleigh, who will personally oversee Luffy's Haki training methods. This ending gives the One Piece story a time skip, which is significant in the development of the series.
For a number of reasons, this arc just happens to be important in the One Piece storyline. This arc acts as a developmental period for Luffy, who shifts from a grief-stricken young man to a more mature and determined individual. The arc is the closing chapter for the Summit War Saga while setting up the next major phase of the story. It depicts the global repercussions of the Marineford War, increasing the scope of the One Piece world while raising stakes for future conflicts.
Moreover, the Post-War Arc is the bridging section between the first and the second halves of One Piece. The character development that transpired did not only pertain to Luffy, but it was for the whole Straw Hat crew—realizing the need to be much stronger. The promise to train for two years shows a huge point: the series' pace is changing, and with this, the attitude of characters toward their dreams and challenges.