The Christa is a highly advanced starship created by a bird-like race called the Lumanians. There are other Lumanian ships that look very much like the Christa.
The Christa is named after Christa McAuliffe, the teacher who died in the explosion of the Challenger shuttle in January of 1986. Why an alien ship would be named for an Earth teacher is still a mystery.
The Christa is ten decks deep (124 feet) and 1157 feet long. When the wings are open, the ship is 600 feet wide; when the wings are closed, she's 350 feet wide. The wings are "solar sails." In space, starts give off solar winds made-up of ion particles, and these winds push the Christa along the same way that wind pushes sailing ships on earth. And there are thrusters in the rear of the ship which help the Christa change direction--so she doesn't fly into a star or something.
The Christa's engines store up ion particles. When they have enough, they can fire the "hyperdrive engines," which push the Christa into hyperspace, so she can go faster than light for a while. If the Christa could never go faster than light, it would take the Space Cases a thousand years to get home! When the Christa goes into hyperspace, her wings close and her neck retracts. The Christa can land on planets.
The Christa was created using what's called "techno-organic" technology. She's sort of a living machine, capable of healing herself when damaged (if the damage isn't too great) and redesigning herself if she feels that it will make life more convenient for the crew. She can also steer herself, but will only do so in the most extreme of situations (such as when she senses a sister ship in distress); she is programmed is to allow the crew to be in charge at all other times. The Christa has at least some degree of sentience. She made her own decision to allow Dram on board, and Thelma indicates that she is able to judge character.