Brandywine is a female, purple-coloured dragon and somewhere between Darm's pet and assistant.
She lives with Darm in his hut amidst the Timbermist Woods. It's questionable and never answered how she is able to enter and leave the hut, which she can since the opening-scene of The Legend of Kyrandia 2 shows her in the Royal Mystics' library and the third game shows her flying upwards towards the player's monitor screen. (Curiously she's "attacking" the player by spitting some firing bursts before noticing that the player's no hostile intruder but a well-known visitor to Kyrandia, so perhaps Brandywine is also some kind of a guardian to the magical world.)
As Darm's assistant she mainly corrects and translates her master's tangling gibberish, jogs his memory, or just helps out in general with useful information. By her tone of voice at times, and how she occasionally rolls her eyes, she's at least slightly annoyed by Darm's - probably age-related - confusion.
Brandywine and Darm behave like some old married couple teasing each other with provoking actions: When Darm reminds her that HE is the Master of Scrolls and Brandon came to him for his advice (because Brandywine intervened and told Brandon all the relevant information), Brandywine spits a flame towards Darm setting his magician's cusp cap on fire. Unimpressed but obviously provoked he drums his fingers on the desk and asks her if he's smelling again some cat-odour from her breath again. Brandywine "shrugs" and asks if it is her fault that she doesn't like knights.
"All sweat and muscles ... and so hard to peel," she complains.