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Betty Grof is a human-turned-wizard woman revealed to have once been the fiancée of a man named Simon Petrikov, who would much later become the Ice King. She and Petrikov were in a committed relationship until Petrikov obtained an enchanted crown, which gradually began to alter his body and warp his mind.
As revealed in "Betty", when Petrikov was wearing the crown for the first time, he chased Betty through a town while shooting ice bolts and asking "Where is my princess?" As he had said "Betty, my princess" in "Holly Jolly Secrets Part II", this likely meant he was looking for her.
It is not clear whether Simon had called Betty "princess" or not prior to wearing the crown, or whether this is a name he affixed to her (much as he began calling Marceline "Gunter") as a result of names whispered to him by the crown.
In "Holly Jolly Secrets Part II", Simon claimed he never saw Betty after his initial time wearing the magic crown (although he may not remember if he encountered her again as Ice King), and he records on video his desperate wish to regain his sanity one day so that he might apologize to her and she might return to him.
In "Betty", Simon regained his sanity after having his ice powers stolen by Bella Noche. Back to normal, he enlisted Marceline, Finn, and Jake to help him create a portal to the past before he drove Betty away, using Hambo as a catalyst. With the portal open, he took the moment to attempt to apologize to Betty, but instead she leapt into the future to be with him, thus explaining why Simon never saw her again in the past.
It was only after crossing through that she learned that Simon was dying. With Bella Noche having stolen all the power from the wizards of Ooo, the magic in the crown that kept Simon from aging was now gone and Death would soon catch up to Simon. Betty took it upon herself to get Simon's powers back to save him from dying. She promised that she would try and find a way to keep him alive and free from the crown's curse. Arriving at Wizard City, Betty defeated Bella Noche (using the advantage of surprise) and restored the powers to the wizards as well as the dying Simon.
She is later seen observing Simon, now the Ice King once again, in his castle (she is noticed by Gunter). She then exits on a flying carpet to begin her search for a way to free Simon from the crown's influence while keeping him from dying.
She was shown listening to Jake's broadcast while working on an experiment in "Jake the Brick".
In "You Forgot Your Floaties", Betty is seen retrieving Grob Gob Glob Grod's helmet from the field and going to Magic Man's house, where she participates in an experiment to help turn Magic Man into the new leader of Mars. Betty has mentioned that since her departure in "Betty", she has been studying how Wizard's powers always determine a degree of madness and sadness in order to find a cure for Simon. As a result of Finn and Jake's intervention during the process of the experiment, Betty ended up receiving all of Magic Man's magic powers (and, presumably, his madness and sadness, as well,) thus becoming a Wizard in the process. She was last seen disappearing through magic yelling, "Laters!" with the same inflection Magic Man had before he lost his powers.
In "King's Ransom", Betty collaborated with a team of foxes to kidnap Gunter, demanding Ice King's crown in exchange. After the exchange, Finn and Jake unsuccessfully attempt to catch the foxes that took Ice King's crown. Betty, can be seen making alterations to the Ice King's crown, before giving it back to him. The Ice King observes that the crown "feels different". This may mean that Betty has not lost all of her sanity, or may have managed to control it, as she had intended, and has begun finding a way to cure Simon's madness.
Betty doesn't make an actual appearance in the series until the episode named after her. In the episode, she is shown to be very loving and devoted to Simon. She is shown to be bold and quick-thinking, as she went to face off against the creature Bella Noche by herself in an attempt to keep Simon from dying. She is shown to be a decently capable fighter, managing to defeat Bella Noche in two hits (though she did have the element of surprise).
Like Simon, she appears to be quite educated in magical artifacts as she was confident she could return Simon to normal. She also co-authored the book Mystic Rituals and Their Space Time Applications with Simon.
Since the experiment-gone-wrong in Magic Man's basement, it appears that Betty's personality may have altered when she became a Wizard. Betty spoke in riddles similar to Magic Man, before an uncharacteristic shriek and yelling, "Laters!".
Betty is an adult woman appearing to have pinkish skin and auburn hair. In a picture on Simon Petrikov's wall, Betty is seen wearing stylish glasses, a green turtleneck and a pair of blue jeans. In another picture, Betty is wearing a lab coat. This might suggest that she was in a field of study, such as science or medicine.
In her Wizard form, she wears a white shirt, grey pants, glasses, green coat, black boots, and Magic Man's hat. Her eyes are white.
Mentioned or pictured
- "Holly Jolly Secrets Part II" (mentioned and pictured; debut)
- "I Remember You" (pictured)
- "Bad Timing" (mentioned)
- "Everything Stays" (mentioned)
- Simon referred to Betty as his princess while he still possessed some of his sanity.
- Adam Muto stated that the figure in the picture with Simon and Betty is "some sort of cryptid." A cryptid is a creature that has been sighted before but whose existence is unconfirmed by science (Big Foot).
- Pendleton Ward and Rebecca Sugar have stated specifically that Betty and Doctor Princess are not the same person.
- Betty's last name is an homage to Stanislav Grof, a psychiatrist who's one of the founders of the field of transpersonal psychology. 
- In the older episodes where she has a brief appearance, her glasses are rounded, but in the episode "Betty," her glasses were pointed at the ends.
- She became a Wizard in "You Forgot Your Floaties."
- Ice King is shown to know who Betty is In Issue 17 and Issue 18 of the Adventure Time Comics, recognizing her, showing sentimentality when finding a picture of the two on what appears to be a date, and breaking into tears when confronting an illusion resembling her.
- Since she absorbed Magic Man's magic, madness, and sadness as well as taking his hat at the end of "You Forgot Your Floaties," she has been often referred to as "Magic Ma'am" by fans, though Adventure Time creators have not shown any signs of embracing the nickname in storyboards and/or AMAs.
- In "Broke His Crown" Betty's AI refers to herself as 'Magic Woman' when Princess Bubblegum believes her to be Magic Man.