Jacket is the fan-given nickname to the romantic pairing between Jack and Juliet. It is part of the love quadrangle featuring Jack, Kate, Sawyer and Juliet. The other parts are known as Jate, Skate and Suliet.
Timeline
Season 3
3x01 "A Tale of Two Cities" - Juliet and Jack meet.
3x02 "The Glass Ballerina" - Juliet brings Jack soup. Ben tells Juliet that she never made soup for him.
3x04 "Every Man for Himself" - Juliet asks Jack to help her with Colleen. Jack can`t save Colleen, when Juliet admits she`s not used to death, Jack comforts her then says he doesn`t care about her.
3x05 "The Cost of Living" - Jack flirts with Juliet after she brings him a cheeseburger for lunch.
3x07 "Not in Portland" - Juliet confesses to Jack that she`s been on the island for more than three years.
3x09 "Stranger in a Strange Land" - Jack saves Juliet from being executed. Jack treats Juliet`s wound with aloe leaves and tells her that they will leave the island together.
3x13 "The Man from Tallahassee" - Juliet flirts with Jack while he plays football with Mr. Friendly. Juliet and Jack work as a team negotiating with Ben.
3x15 "Left Behind" - Juliet bests Kate in knowledge about Jack. Jack tells Sayid that Juliet is coming back to the beach with them.
3x16 "One of Us" - Jack protects Juliet from the rest of the camp. Juliet asks Jack why she doesn`t have to explain herself to him. He tells her because he saw it in her eyes, that she wants to leave the island more than anything.
3x17 "Catch-22" - Jack and Juliet flirt over dinner.
Mx05 "Operation: Sleeper" - Juliet confesses to Jack that she is still working for Ben. He is visibly upset.
3x19 "The Brig" - Jack and Juliet eat together. When Kate interrupts, Juliet says they should tell Kate something, but Jack insists that the shouldn`t.
3x22 "Through the Looking Glass" - Juliet kisses Jack before heading out with Sawyer in what looks like a suicide mission.
Season 4
4x02 "Confirmed Dead" - Juliet and Sayid save Jack and Kate. Jack and Juliet flirt, and Jack protects Juliet from Miles.
4x06 "The Other Woman" - Juliet admits to Jack that she has feelings for him. In response, Jack kisses Juliet. ("The Other Woman")
4x10 "Something Nice Back Home" - Juliet saves Jack`s life by performing an emergency appendectomy. After the surgery, Juliet tells Kate about their last kiss, telling her that Jack kissed her more to convince himself that he "wasn`t in love with someone else." When Kate leaves, Juliet tells Jack that she knew he was awake [to hear their conversation].
4x11 "Cabin Fever" - Juliet scolds Jack for being up so soon after his surgery.
4x12 "There`s No Place Like Home, Part 1" - Juliet and Jack fight about Jack`s intention to follow the helicopter. Juliet warns Jack he is still in recovery from his appendectomy. When Jack still prepares to leave, she emotionally tells him not to "bleed to death" and storms off.
Season 5
5x09 "Namaste" - Jack and Juliet reunite with a warm hug.
5x11 "Whatever Happened, Happened" - Juliet confronts Jack after he refuses to help her save young Ben.
5x13 "Some Like It Hoth" - Jack and Juliet have coffee while waiting for Sawyer to return home.