Angel Beats! is an emotional, heartfelt anime.
Quick to the point, (this is an extensive review but this is the reason it is the 4/5 and not another rating) this anime is beautiful and has the story arc, music (Angel Beats! music is really good, the upbeat ones and the downbeat ones (pun intended)), character design, and voice acting. All the elements fit together so nicely and makes a lot of sense, the only thing is; the 13 episodes isn't enough to make you really sympathetic towards the major SSS characters, even though 13 is enough you get you close to them emotionally and accomplishes that goal, and restless.
Everyone is dead in a level of the afterlife, limbo. Limbo is a state where restless souls are put because these souls curse god "a cruel life" and "It isn't fair". Their soul, their literal essence of existence and what makes a person exist, has not completed its goal. When a soul is at peace, they transcend onto their next life. Angel Beats! is about these badass souls that had a life, unlike the "NPCs" that exist because they're lost, soulless, they're not a person, were not a person. These souls, the SSS, fight Angel because they aren't at peace with their lives, and don't accept it. Limbo is where they complete their soul's goal, in the most real way possible (limbo is the afterlife, but it's still "life".)
Angel Beats! an awesome Anime that is a MUST WATCH for anyone. Angel Beats! is one of those rare animes that are hard to find, in a good way.
Now, some people are confused and ironically, aren't at peace, like the rest of the souls. If you watch the entirety of the final episode, you will understand and finally be at peace and understand.
Yuzuru died before Angel, however Yuzuru was at a higher level of the afterlife, waiting to be thanked by Angel, here's why; Angel was given a heart transplant, and that heart was Yuzuru's heart. Angel never thanked him and so she went to limbo because she had a regret, not thanking the donor that had basically, given her life. When she thanked him, and was confessed to by Yuzuru, that he loved her, she would finally be at peace. Now, just like the souls that are at peace and at terms with their death and ready to move on into their next life, we move with them because we are at peace with the resolution with the show, standing with them during their graduation.
Angel hums a song for apparently, no reason, HOWEVER, post-credits onto the end scene (watch the entire final episode) this girl that looks a lot like Angel hums the EXACT SAME SONG, with this man that looks bizarrely like Yuzuru, goes and can safely assume, talks with her. Unspoken, the other major SSS characters probably reunite, because after all, their friendship was carved into something greater than a physical "love" but their literal existence, their soul, their friendship.
You could say Yuzuru is the bootleg god because later on, he asks the angel (Angel) for help to bring everyone to peace and move on, which she accepts to help. This last part was something that is not cannon in any way shape or form, just something symbolic I picked up during my watch of Angel Beats!