Nyssa is from the planet Traken, a member of the Traken Union where peace and harmony prevail and evil cannot survive. The planet is watched over by a Keeper, who requested the Doctor's aid when he saw terrible danger in his planet's future. This danger turned out to be the Master, who failed in his attempt to seize the position of Keeper for himself but succeeded in taking over the body of Nyssa's father, Tremas, one of the Consuls of Traken. Nyssa did not leave with the Doctor straight away, but a projection of his fifth incarnation brought her to the planet Logopolis to help with the crisis there.
Nyssa's Trakenite upbringing has instilled in her an aristocratic bearing and great serenity. Because of this, when the Master stole her father from her and then, soon after, she learned that her homeworld had been completely destroyed by one of the Master's schemes, Nyssa did not succumb to her grief; instead, she grieved the loss of her father and her world quietly and stoically, and only revealed her true anger when she confronted the Master.
Despite her tranquil upbringing, Nyssa has a deep core of inner strength. Not as timid as she looks, Nyssa is always ready to do what she has to in order to help the Doctor, whether this means sneaking around to break him out of prison or stunning people with a weapon she has picked up.
Nyssa is highly talented in bioelectronics, an expert in cybernetics, and she understands bioengineering, though she knows so little about telebiogenesis, and her keen scientific mind is very useful to the Doctor. Part of her room is set up as a scientific laboratory, where she often runs tests. One of her favorite instruments is a Trakenite ion bonder, a tool for molecular adjustment which can be used for a variety of purposes, including a stunning weapon if the ion rate is stepped up. She can also pretty well pilot the TARDIS. But despite her rather serious upbringing as a member of the Trakenite court, Nyssa enjoys having fun, and her training in Traken courtly dances, at which she is quite good, have given her the ability to quickly and effortlessly pick up other dancing styles.
Her calm demeanor and gentle rationality also help her to defuse some of the tension that commonly builds up between the sullen Adric and the argumentative Tegan, especially when one of them is arguing with the Doctor. Nyssa and the fifth Doctor are of very like minds, and often she can get through to him when none of the others can. Nyssa is also an extremely trustworthy person.
Nyssa also seems to have some latent psychic ability, which is augmented when she is in the vicinity of highly-psychic beings like the Xeraphin. This imparts to her a kind of sixth sense for danger, a higher receptivity to communicating with telepathic beings and serving as a conduit for them, and a greater resistance to hypnotic influences. This ability, however, rarely manifests itself.
Nyssa has curly brown hair and blue eyes. Initially, she stays in her Traken court clothes: a buttoned velvet bodice with puffed sleeves, diaphanous skirt, and heeled shoes, with a fur muff and tiara. Nyssa eventually decides to change in the skirt and shoes for matching velvet trousers and heeled boots, and the tiara and muff are lost and abandoned, respectively, on Castrovalva. (She apparently does recover the muff on the way back.) Eventually Nyssa gets more daring with her outfits, even going so far as to traipse around in her underwear (or something very much like it)!
Nyssa finally leaves the TARDIS crew when it lands on Terminus, a giant leper colony for people afflicted with Lazars' Disease. Appalled by the treatment of the people and filled with a desire to help, Nyssa elects to stay behind and do what she can in search of a cure.