Burt believes that Kurt's biological mother is there watching over them as shown in Preggers, the fourth episode of Season One, and it is assumed that he is a Christian because in Furt, the eighth episode of Season Two, Burt and Carole got married in a church. However, Kurt is an atheist, as revealed in Grilled Cheesus, the thirth episode of the same season, and so believes that his mother only lives through the impacts she has made in her life on the earth.
She was first mentioned in the Season One episode, Preggers, when Burt told Kurt that he wished Kurt's mom was at the game. He said that she would have been proud of Kurt.
Burt says that Kurt is strong like his mother.
Kurt tells Finn that there is an old dresser of his mother's that still smells like her perfume. Kurt says that sometimes he just lies down in the room and smells her. He also says, "My mom died ten years ago, and he still keeps her toothbrush on the holder by their sink." That would potentially imply that his mother died when he was around age six. Kurt saying "ten years ago" may have been him rounding, however.
When Will asks the glee-clubbers how they answer the phone, Kurt answers, "No, she's dead; this is her son," morbidly referencing her death, and also showing that he sounds like she did when she was alive.
It is revealed that until Carole, Burt has not dated anyone since Kurt's mother died, marking an eight year span of Burt being without a woman in his life. This is the episode where Burt reveals that Kurt's mother has been dead for specifically eight years.
Kurt says that he felt like his life was over when his mother was being lowered into the ground, and later in the episode, a younger Kurt and Burt are seen via flashback visiting her grave.
Burt calls her the "love of his life," saying it killed him inside that not only did he become a widower, but that Kurt also lost his mother.
Burt associates Kurt's compassion and moral fortitude to his mother when speaking to Blaine about whether Kurt needs to have 'The Talk' with his father.
While burying Pavarotti, Blaine asked Kurt if the burial reminded him of his mother's burial, to which Kurt tells him that the casket was bigger, but it was otherwise the same.
Burt arrives in New York for Christmas as a surprise to Kurt and Rachel, he also brings a tree and some gifts. When they place the tree down, Burt explains to Rachel that Mrs. Hummel always bought the tree and he always told Mrs. Hummel to wait till he got home from work to buy it but she never could. The first Christmas after Kurt's mom died, Burt totally forgot about it, not until he saw a little Kurt hanging his own version of a small Christmas ornament on his window shade on Christmas Eve. Kurt listens as he walks towards the box of ornaments and grabs a perfume bottle ornament and says he loves how she smelled. So after the events of hanging the ornament on the window shade, Burt went to buy a tree at a Christmas sale and it was Kurt's first smile since his mother died. Rachel gets all teary but Kurt tells her off by saying "No tears on Christmas Eve!"
Kurt's inner thoughts include that his dad is the only thing that got him through his mom dying.
While Burt is taking Kurt to his surprise proposal, he talks about his relationship with Kurt's mom. He says they met when they were 22 and he asked her to marry him only six months after. Burt also says that he wouldn't have waited more to do that and he would have wanted to meet her ten years earlier instead. He says that he misses her so much that he could do anything to take her back for even only ten minutes, and tells Kurt he thinks they are too young but he and his mother were young and he doesn't regret it.
Kurt mentions to Clara Banks that Mrs. Hummel died when he was eight years old and that throughout his life he used to pretend that she was alive.