Doctor Who: The Newbies Guide
This is the second story in Season 20.
The Fifth Doctor is physically younger than his previous incarnations. He wears Edwardian cricketing clothes with a stick of celery on the lapel. He is less eccentric than his previous incarnations. In Earthshock he was unable to save his companion Adric from dying.
Nyssa of Traken is the daughter of Tremas of Traken. In The Keeper of Traken she helped the Doctor and Adric to defeat the Melkur, a living statue that threatened their planet. The Melkur was actually the Master's TARDIS, and at the end of that story the Master took over her father's body. In Logopolis, the Master destroyed a large portion of the universe, including Traken.
Tegan Jovanka is an Australian air stewardess who accidentally stumbled into the TARDIS in Logopolis. She has a tendency to moan. In Kinda she was possessed by psychic entity called the Mara. In Time-Flight she was left behind in her native time, but she rejoined the Doctor when she ran into him in Arc of Infinity.
Recurring and Historical Characters
The Mara is a psychic entity that takes the physical form of a snake. In Kinda it possessed Tegan in an attempt to become real and take over the planet of Deva Loka. The Doctor was ultimately able to fight it off, and Tegan believed it was gone from her mind.
It helps if you are familiar with the Mara's previous appearance in Kinda.