Vicki was the first new companion to join the regular crew of the show
Doctor Who. She is played by Maureen O'Brien.
Vicki was a teenage girl when first encountered in The Rescue, stranded on the planet Dido. she left Earth with her father in 2943 after her mother died. They were heading with a colony ship to the planet Astra, until the ship crashed. After dealing with the insane Bennett The Doctor took her under his wing, and she travelled with him and his friends in the TARDIS.
Vicki was a better character than the departed Susan, and was generally easier for people to accept, while still fulfilling some of the same plot roles (screaming, needing to be rescued, etc). She interacts with the other characters much better and doesn't cause so much mayhem as her predecessor.
The highlights of Vicki's travels with The Doctor include meeting Nero and King Richard, landing on the Marie Celeste, helping save a Viking fleet from a tactical nuke (in 1066, no less), and being hailed as a prophetess in the city of Troy, remaining in the Earth's past after the destruction of the city.
Don't just stand there and scream, you little fool, run! - Ian, saying what's on the viewers mind; The Chase
The real life reason for Maureen O'Brien leaving the show was the producer didn't like her complaining about her dialogue in the story Galaxy 4 (it was crap dialogue). She returned from a holiday and found she was to be written out at the end of the next story. She hadn't been happy with the series but it would have been a shock as her contract had been reissued with an option for twenty more episodes. O'Brien went back to teaching, which had been her first career choice before a friend landed her a role in Doctor Who.
The story reason was the usual "Fallen in love with random male character" which seems very dated these days. It was used because it was the quickest way to write a character out when an actress turned up one morning and said "I'm quitting" or the people in charge got the snit with someone. O'Brien and the actor playing her spontaneous love interest reputedly thought this was ridiculous because.... they had hardly any scenes together! The story goes they insisted on adding more scenes of the two talking, and also eyed each other up in other scenes. So even if the reason for the character's departure is archaic at least it was done better than it would have been.
There's a huge gallery of stills from her episodes here:
http://www.shillpages.com/dw/obrienm.shtml
Note that when she took the role Maureen O'Brien was 21, playing someone who was 16.