Davros is the insane and evil wheelchair-bound creator of the Daleks and one of Doctor Who's many enemies. He is quite hideous to look at, with a shriveled face and a permanent scowl. Despite creating them, he has had a love/hate relationship with the Daleks. Often they turn on him, showing very little gratitude. He is always looking to create a new breed that will be totally loyal to him. Like his creations, he is unable to climb up stairs because he moves around on wheels.
Davros is a Kaled from the planet Skaro. On Skaro, back in the day, the Kaleds and the Thals were two humanoid races co-inhabiting the planet. Naturally war broke out, and the result was that the planet was left a nuclear wasteland. Both the Kaleds and the Thals had to live underground. Davros was the head scientist of the Kaleds, and he had a clever plan to defeat the Thals. He mutated the Kaleds (and boy did he mutate them -- they went from being humanoid to being some sort of green blob with a lot of tentacles) and then built them an armored exoskeleton in which to exist. The mutated Kaleds plus their armored exoskeleton became known as Daleks. Davros himself declined to be mutated, and instead just confined himself to a robotic wheelchair that also provided him with life-support function. The Doctor intervened before Davros could destroy the Thals. He and the Thals sealed up Davros and the Daleks in their underground city on Skaro. (This story was documented in the episode Genesis of the Daleks.)
Of course, some Daleks escaped and began spreading terror around the universe. At one point the Daleks went to war with a race called the Movellans. Both the Movellans and the Daleks operate on a robot-like logic. Thus they were at a stalemate, and both of them concluded that they could only win if they could get control of Davros. They both traveled to Skaro and tried to dig him up, but the Doctor again interfered with their plans. Davros was captured and was taken away to Earth to be tried for his past crimes by the humans. On Earth Davros was sentenced to a lifetime of suspended animation. (This was documented in the episode Destiny of the Daleks.)
Approximately 90 years after Davros' trial, the Daleks payed the human Commander Lytton to help break Davros out of jail. It seems that the Movellans had infected the Daleks with a virus, and Davros was the only person who could cure it for them. The Doctor again tried to save the day, but this time Davros managed to escape and begin making more Daleks. (This was documented in the episode Resurrection of the Daleks.)
Davros made the planet of Necros his new home. He masqueraded as someone known as the Great Healer, and created Daleks from bodies in suspended animation. Always cursed with bad luck, the Doctor found him and unmasked him. The original Daleks (not the ones Davros was making from the bodies) captured him and return him to Skaro. (This was documented in the episode Revelation of the Daleks.)
Later on (well, technically back in 1963, but time travel was involved) Davros ends up leading one faction of Daleks against another faction of Daleks for control of the Hand of Omega. Davros is calling himself Emperor Dalek by this time, even though he isn't really a Dalek at all. If you couldn't guess, the Doctor saves the day and defeats both factions of Daleks. Davros manages to escape, as always. (This was documented in the episode Remembrance of the Daleks.)
That was the last appearance of Davros in the television series. However, in 2000 Big Finish Productions got permission from Terry Nation's estate (Terry Nation created the Daleks) to include the Daleks in their Doctor Who Audio Adventures. For some reason they were forbidden from using Davros, but some fans are agitating for his return.
Davros appeared in the following TV episodes:
Sources:
http://www.thelogbook.com/tardis/dalek/
http://www.lofficier.com/dwudd.html
http://www.mentalis.f9.co.uk/DWID/Species/Daleks/
Many hours watching PBS as a child