Abigail and Shawn had a bit of a fling back in high school. Shawn pursued Abigail throughout their entire senior year until Abigail agreed to go on a date with him. However, Shawn never showed. He went to meet her and saw her, but got too nervous, and eventually choked and stayed hidden from her view. Abigail waited around for an hour before she left, disappointed.
Thirteen years later, at their high school reunion, in the episode "Murder? ... Anyone? ... Anyone? ... Bueller?", Shawn and Abigail met once again. She was still upset with him for standing her up, and was unimpressed by his excuse (he claimed that he was a midwife), or Shawn's supposed psychic abilities. When Shawn sees a body fly off the roof, she, as well as Gus, remains unconvinced that a murder took place. So Shawn goes out and tries to find proof that a crime was committed as well as find a way to patch things up with Abigail. Shawn eventually unveils the killers and impresses the formerly skeptical Abigail. Then he goes and tells her why he really stood her up. This leads them to share a kiss, but Shawn and Abigail both seem fine with leaving their relationship there.
Later, in "An Evening with Mr. Yang", Shawn calls up Abigail, after Gus tells him that Shawn will be eighty years old and still hitting on waitresses and that his game is tired. Gus then tells him that Abigail is a real person and that he hopes that he wasn't using Abigail just to prove a point. Throughout the rest of the episode, Shawn is forced to postpone the date, which causes Abigail to worry because she doesn't believe that Shawn is chasing a serial killer. However, she probably starts to believe him when a protective detail shows up at her place later. When Shawn nabs Mr. Yang, he has Abigail brought to the drive-in theater where he has arranged a private showing of a movie. When Shawn is getting the popcorn, Juliet shows up and asks Shawn out on a date, revealing her feelings for him. Shawn reluctantly turns her down and goes outside to rejoin Abigail, who then asks him if something is wrong. Shawn tells her that everything is not all right because the theater is out of butter for the popcorn. Abigail is relieved and they go into Gus's car to enjoy their date, which is promptly interrupted by Gus, who will not let Shawn use the car unless he himself is in it.
In season four, Abigail returns as Shawn's girlfriend. During this season, their relationship causes a lot of tension between Shawn and Juliet. It is clear that Shawn still has feelings for Jules since he gets very jealous when she goes undercover as a client's girlfriend in "Bollywood Homicide". During that same episode, when Shawn risks his life to save Juliet in front of Abigail, she is impressed that he would do that for a "random co-worker". Shawn plays it down to avoid suspicion. In "You Can't Handle This Episode", Abigail leaves for Uganda. Shawn is very distressed, but they try to maintain a long-distance relationship. In "Death Is in the Air", Shawn plans to reveal his feelings to Juliet but is interrupted unintentionally by Lassiter. It is unclear how this would have figured into his relationship status with Abigail. Finally, in "Mr. Yin Presents...", Abigail breaks up with Shawn after she is kidnapped by Mr. Yin. She says that she wants to get away from the danger because she wants to do so much with her life but she can't do anything if she's dead. However, she does tell Shawn to call her if he ever stops chasing criminals. She does not reappear thereafter (until the Psych After Pshow).
The gallery page for Abigail Lytar can be found here.