The Doctor is a Time Lord from the planet Gallifrey, who stole one of the TARDISes long ago to go exploring. Due to his physiology, he is capable of "regenerating" after dying due to mortal wounds or old age, essentially changing appereance and personality(though his memory and basic mindset remain the same). It is hinted that he is capable of regenerating 12 times.
The Doctor usually travels with 1-3 companions or assistants who eventually leave him either by dying, choice or force.
The show features many recurring villains with varying goals. The most well-known of these are the Daleks(squid-like creatures inside war machines) who usually attempt to exterminate the universe of any other species other than their own; the Master, a renegade Time Lord driven insane by a constant drumming in his mind. He is obsessed with taking over the universe/causing pain to the Doctor; the Cybermen who try to assimilate all races into their own.
In the 2005 restart of the series, it was revealed that a massive Time War was fought between the Time Lords and the Daleks which ended with the Doctor obliterating both races to preserve the universe. The Doctor feels massive guilt over his actions and tries to make up for what he did to the best of his abilities.