Betty Riker was the wife of Kyle Riker, and the mother of William T. Riker. (TNG: "Conundrum") She died in 2337, when Will was two years old, and therefore never got to know his mother. (TNG: "Time Squared", "Interface") One of Betty's final requests was that Kyle raise Will in Valdez, which he did. (TNG: "The Icarus Factor")
Never being able to know Betty while growing up, everything her son Will knew about her was taken from pictures and the stories her husband told their son; stories Will begged his father to tell, over and over. In 2340, when Will was five years old and started school, he began to tell his new friends the same stories about his mother that his father told him, as if she was still alive. Eventually, he told the stories about her so often, he began to believe them, and that she had just gone away but was coming back. Soon, his teacher learned of this problem, and both she and Kyle had to talk to Will and make him realize that his mother was dead and she was not coming back. In his mind, that was the day his mother actually died. Will cried the entire night following, but later realized it was an important step in accepting his mother's death. (TNG: "Interface")
Betty's death was very traumatic for Kyle and the only thing which kept him going was Will, although he did not reveal this fact to his son. The memories of Betty's presence at their Alaska home were painful for both, and this initial trauma created a rift between the two Rikers which would last fifteen years. (TNG: "The Icarus Factor")
Background
Betty Riker's name was never spoken in dialogue, but was established in a biography screen prepared for Will in "Conundrum", although it was not seen in the episode. "The Icarus Factor" implies the cause of her death was sudden, and may have been due to an illness.