Soon after their wedding, John and Jenny Grogan (Owen Wilson and Jennifer Aniston) escape the brutal Michigan winters and relocate to a cottage in South Florida, where they are hired as reporters for competing newspapers. At The Palm Beach Post, Jenny immediately receives prominent front-page assignments, while at the South Florida Sun-Sentinel, John finds himself writing obituaries and two-paragraph articles about mundane news like a fire at the local garbage dump.
When John senses Jenny is contemplating motherhood, his friend and co-worker Sebastian Tunney (Eric Dane) suggests the couple adopt a dog to see if they're ready to raise a family. From a litter of newborn yellow Labrador retrievers they select Marley (named after reggae singer Bob Marley), who immediately proves to be incorrigible. They take him to Ms. Kornblut (Kathleen Turner), who firmly believes any dog can be trained, but when Marley refuses to obey commands, she expels him from her class.
Editor Arnie Klein (Alan Arkin) offers John a twice-weekly column in which he can discuss the fun and foibles of everyday living. At first stumped for material, John realizes the misadventures of Marley might be the perfect topic for his first piece. Arnie agrees, and John settles into his new position. Marley continues to wreak havoc on the household, providing John with a wealth of material for his column, which becomes a hit with readers and helps increase the newspaper's circulation. Jenny becomes pregnant, but loses the baby early in her first trimester. She and John travel to Ireland for a belated honeymoon, leaving the rambunctious dog in the care of a young woman who finds him impossible to control, especially during the frequent thunderstorms that plague the area. Soon after returning from their vacation, Jenny discovers she is pregnant again, and this time she delivers a healthy boy, Patrick. When she has a second son, Connor, she opts to give up her job and become a stay-at-home mom, prompting John to take on a daily column for a pay increase. Due to the crime rate, the couple decides to move to a larger house in the safer neighborhood of Boca Raton, where Marley delights in swimming in the backyard pool.
Although she denies she is experiencing postpartum depression, Jenny exhibits all the symptoms, including a growing impatience with Marley and John, who asks Sebastian to care for the dog when Jenny insists they give him away. She quickly comes to realize he has become an indispensable part of the family and agrees he can stay. Sebastian accepts a job for The New York Times and moves away.
John celebrates his 40th birthday and later goes skinny dipping with Jenny in their swimming pool. Increasingly disenchanted with his job, he decides to accept a position as a reporter with The Philadelphia Inquirer with Jenny's blessing, and the family moves to a farm in rural Pennsylvania. John soon realizes that he is a better columnist than reporter and pitches the column idea to his editor. Life is idyllic until the aging Marley begins to show signs of arthritis and deafness. An attack of gastric dilatation volvulus almost kills him, but he recovers. When a second attack occurs, it becomes clear surgery will not help him, and Marley is euthanized with John at his side. The family pay their last respects to their beloved pet as they bury him beneath a tree in their front yard.

Question: What did Jenny quickly realize after trying to give Marley away?
Answer: That Marley had already become and indispensable part of the family.
Alternative answer: Jenny comes to the realization that Marley is a huge part of their lives.