Victor tells Captain Walton the story of his father's marriage because he believes that the "circumstances [...] illustrate his [father's] character." Victor's father had a friend named Beaufort who "fell [...] into poverty," and grew so embarrassed by his fallen state that he moved away to Lucerne, Switzerland, with his daughter, Caroline. Mr. Frankenstein genuinely cared about his friend and tried hard to find Beaufort. In the meantime, Beaufort grew quite ill and was taken care of by his daughter "with the greatest tenderness." Caroline's "courage rose to support her in her adversity" and she worked to earn enough, at least, to support herself and her father, though meagerly. Beaufort finally died, and Caroline was weeping over his coffin when Frankenstein entered the house. Despite their age difference, Victor says,

There was a sense of justice in my father's upright mind which rendered it necessary that he should approve highly to love strongly [....]. There was a show of gratitude and worship in his attachment to my mother, differing wholly from the doting fondness of age, for it was inspired by reverence for her virtues and a desire to be the means of, in some degree, recompensing her the sorrows she had endured, but which gave inexpressible grace to his behaviour to her.

In other words, Frankenstein seems to have been deeply affected by seeing Caroline's resourcefulness and devotion to her father. She managed to survive in poverty, when she had been used to such a different lifestyle, and these qualities provoked a genuine love for her. He appreciated her virtues and seemed to want to repay her for her devoted suffering: he wanted to make her happy after she'd experienced such sorrow and pain.

The story of Victor's mother and father is important because it sets up the idea of duty, something that Victor will fail in later in in the book.  Victor's mother was the daughter of a man named Beaufort, who had been a business partner and friend of Victor's father.  Beaufort falls on hard times, becoming very poor and sick.  Victor's father seeks out Beaufort, and finds him and Caroline (his daughter) just as his old friend has died. 

In concern and compassion, and in duty, Victor's father takes Caroline under his wing, placing her with a relative to ensure that she was well cared for.  Victor just tells us that two years later they married - we can assume that as she lived with the Frankenstein relatives, Victor's father visited with and fell in love with her.

There was a considerable difference between the ages of my parents, but this circumstance seemed to unite them only closer in bonds of devoted affection. There was a sense of justice in my father's upright mind, which rendered it necessary that he should approve highly to love strongly. ...There was a show of gratitude and worship in his attachment to my mother, differing wholly from the doting fondness of age, for it was inspired by reverence for her virtues, and a desire to be the means of, in some degree, recompensing her for the sorrows she had endured...

The above quote suggests that the affection between them was genuine.  It also shows that "justice" is part of what pushed Victor's father towards marriage, added to an appreciation for his mothers "virtues" and for her hardships.