Shutter Island" (2010) is a action adventure movie starring Leonardo DiCaprio and, because of its plot, requires a "Shutter Island" (2010) explanation. There are several layers to a "Shutter Island" (2010) explanation that you need to understand in order to understand the movie. It also helps to know the roles of the key characters when trying to understand this "Shutter Island" (2010) explanation.
What is the "Law of Four"? This is important to understand as part of a "Shutter Island" (2010) explanation because it explains the existence of two of the main characters. The "Law of Four" referes to the fact that two names actually indicate four people because they are anagrams. If you rearrange the letters of the name of the main character, Edward Daniels, you get the name of the person who Daniels actually is, which is Andrew Laeddis. The maiden name of Laeddis' wife, Dolores Chantal, can have her name rearranged to spell out Rachel Solando. Rachel Solando is the patient who supposedly escaped from Shutter Island.
Which one is real; Andrew Laeddis or Edward Daniels? Part of an effective "Shutter Island" (2010) explanation is establishing who the main character really is. Leonardo DiCaprio is playing Andrew Laeddis, who is a former federal agent who murdered his wife. Laeddis so despised himself for what he had done that he changed his name to Edward Daniels and believed that Andrew Laeddis was a different person who killed his wife.
Was George Noyce Real? George Noyce (Jackie Earle Haley) was a real person who's name was really George Noyce. But the part of the "Shutter Island" (2010) explanation that is important to understand is that Noyce was planted in Ward C by the doctors trying to treat Laeddis. Noyce was real, but his incarciration in Ward C was not.
Did Teddy (Andrew) really talk to Dr. Rachel Solando in the cave? Chances are that he did not. Solando was created by Laeddis' mind to verify everything he thought he already knew. Once Solando told Teddy everything he wanted to hear, he went to sleep. When he woke up, no trace of Solando was seen in the cave.
What happened at the end? At the end of the movie, Andrew finally admitted that he was Andrew Laeddis, that Teddy was imaginary and that he did kill his wife. Dr. Cawley (Ben Kingsley) was trying to prevent having to give Andrew a lobotomy, which was standard treatment for severely disturbed and dangerous patients back in 1954, when this movie is set. But, the next day, Andrew regressed back into being Teddy and Dr. Cawley reluctantly ordered the lobotomy.