Adelaide was a child during the Daleks' invasion of Earth in 2008. She was spotted by a lone Dalek, but it unaccountably spared her. The Doctor thought the reason was that the Dalek recognized her as a "fixed point in time."
Adelaide is only a companion for one story, "The Waters of Mars", but it's quite a story. She's the comander of Bowie Base One, the first Earth colony on Mars. A Martian virus/disease called "The Flood" is infecting the crew and Adelaide struggles to save them but is losing ground. The Doctor shows up outside on the Martian surface in a serious color contrast between the bright blue TARDIS and the bright red Martian landscape. Of course the Doctor could save them, but he uncharacteristically just mopes around saying, "I should leave" and doesn't do much. Later we learn that, like the story "The Fires of Pompeii", Bowie Base, and Adelaide in particular, are a "fixed point in time" where the entire base is destroyed and the crew, including Adelaide, are wiped out. The Doctor can't change that event without drastically changing the future of the Earth and maybe more than that.
Then something shocking happens, he does save them! He takes the remaining crew of Bowie Base, including Adelaide, back to Earth in the TARDIS, violating the Laws of Time! His explanation is that since he's the last of the Time Lords and the Daleks are gone, He won!, He's the last man standing! The Time Lord Victorious! and as such, he makes the rules of Time from then on. "It's taken me all these years to realize that the Laws of Time are mine...AND THEY WILL OBEY ME!" says the Doctor. Clearly not the Doctor we know at all.
When all of this is explained to Adelaide, particularly the Doctor's explanation of the reasons for his actions she says, "I don't care who you are, The Time Lord Victorious is wrong!" She then goes into her home seeming to reach for a weapon as she goes through the door. There's a flash of energy indicating that she has just committed suicide and the timeline returns to it's correct state..
Adelaide is played by Lindsay Duncan (born Nov 7, 1950 in Edinburgh, Scotland). She has a boxfull of best actress awards and nominations for stage, TV, and movie roles. The one I most remember is "Under a Tuscan Sun." Keep up the good work, Lindsay.