the doctor is a timelord. his ship can travel through time and relative dimensions in space. the chameleon device that allowed his ship to appear as anything in order to blend in with any location is broken so the ship is stuck in the shape and outwad appearance of a british police phone box circa 1960.
the doctor is a little bit of a renegade. his people laid down rules of engagement regarding dealings with alien races and situations. the doctor disagreed with those rulings/laws and often ran in conflict with his people.
The doctor encountered the daleks and thus his greatest foe and successfully defeated them several times until the final battle where he destroyed them all at the cost of also destroying his own people.
he has a deep affection and vested interest in the people of earth because he believes that Earth people are basically good people who can go far and do good things with guidance. And seeing as he has no home planet to go to he seems to like returning to earth as a rest stop and usually fixes some small problem like megolomaniac alien invaders hellbent on destroying the earth or the bizarre return of the daleks thanks to meddling individuals/organisations.

The doctor can be very preachy, very opinionated, very wrong. but he has his hearts in the right place and always believes his actions to be for the betterment of mankind or the particular alien race/species he is around at the time. He believes in the rights of the individual and liberty, egality and equality. Though at times will pretend not to be concerned with such issues.

over the yeas he's taken onboard various 'assistants' who he seems to treat fairly badly but in actual fact like a skilled tutor teases great strength and fortitude out of these individuals. many of them earth dwellers originally.

The show was originally intended as light entertainment. had no budget and incredibly limiting technology was used to produce the show. the ingenuity and creativity of cast and crew plus the writers brought something fresh to the small screen. nothing like Dr Who had ever been seen before at its time of launch.

the ingenious device of having the doctor regenerate when different actors took on the role meant longevity with little interruption to the flow of the show. it allowed for a segue between different actors and didn't really alienate any viewers.

the show was made with tongue firmly in cheek. but with deep affection. the wobbly sets and dodgey costumes on aliens made it amusing and entertaining to adults and kids hid behind the sofa scared witless by the daleks and cybermen etc. generations grew up watching the show and it became a british institution almost.

it was cancelled just as it was starting to really find it's feet in terms of utilising technology to enhance the show but also at the point where no-one was really taking it seriously anymore due to poor writing and ridiculous scenarios. however, after the made for TV big budget movie version which went down ok it was felt that the time was right to bring back the doctor and pimp da show.

The latest incarnation takes parts of the history of the old show and weaves it into the 'lore' but embelishes upon that lore and thus moves the story arcs forward. re-using old foes but presenting them in a way that is palletable to modern audiences.

Doctor Who has never been serious sci-fi. it's not in the same league as say star trek or babylon 5 or stuff like that. it's still aimed at kids with the odd wink to camera for adult viewers. it's just supposed to be entertainment pure and simple. the science is bogus but sounds good when said really fast in a tense situation. the scripts are shakey and have amazingly huge plot holes.
However the actors put a lot into it and the creators are enthsed and passionate about the show and it makes for reasonably good viewing.

it takes a while for this modern version to get going. there was a lot of conservative moves forward with Christopher Ecclestones doctor, allowing an audience to get used to him and the new show. but now the tone is set and production values are fairly high, it can grow and go places. It still has a low budget it sill has wobbly sets and sometimes dodgey costumes, but the premise is the same, drama/tension/strange happenings/alien encounters/danger/suspense/sleuthing/and pushing the boundaries of what can be achieved on a small budget for TV that looks good and entertains.

the role of rose and her mother and mickey was to draw in the family viwing unit. to base part of the show in an earthly location and allow viewers to comfortably associate with those characters and make the journey with them through the first season. in the second season having done that we get to relax and move away from that some. in the third season there will be changes. it will or should feel more like the original version of the show and be a little easier to follow.

and I know I've summarised badly but I'm no expert. just think of the doctor as a time travelling, spaceship driving, galactic hero, battling detective, IT expert. with foxy sidekicks and a robot dog. he has two hearts and when he faces death he cheats it by regenerating his body and assuming a new one.
In a sense he's a god. or universal deity. lonely and capricious. impish. he struggles to deal with all he knows and has seen or done. has big guilt trips and suffers from bipolar syndrome probably. he cares deeply about issues of right and wrong and especially injustices. he's ancient. so old to count the millions of candles needed on his birthday cake he'd need assistance.
He's managed to get out of more scrapes and dangerous situations than the mission impossible team ever did and only ever used a sonic screwdriver. it opens locks, it opens things with screws, it emits frequencies usefull in recalibration of various sci-fi devices. his taste in clothing is spotty. but getting better.

*breathes*

how am I doing?